Generalized Stirling_2 Triangle k = -6 | ||||

Sum: A049412 | all partitions: A134278 | ~ by length: A049385 | ~ by biggest part: A157396 | diagonal: A008548 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

7 | [1,6] | [6,1] | [1,6] | 6 |

85 | [1,18,66] | [66,18,1] | [1,18,66] | 66 |

1465 | [1,36,108,264,1056] | [1056,372,36,1] | [1,144,264,1056] | 1056 |

32677 | [1,60,540,660,3960,5280,22176] | [22176,9240,1200,60,1] | [1,600,4620,5280,22176] | 22176 |

Generalized Stirling_2 Triangle k = -5 | ||||

Sum: A049120 | all partitions: A134273 | ~ by length: A049029 | ~ by biggest part: A157397 | diagonal: A007696 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

6 | [1,5] | [5,1] | [1,5] | 5 |

61 | [1,15,45] | [45,15,1] | [1,15,45] | 45 |

871 | [1,30,75,180,585] | [585,255,30,1] | [1,105,180,585] | 585 |

15996 | [1,50,375,450,2250,2925,9945] | [9945,5175,825,50,1] | [1,425,2700,2925,9945] | 9945 |

Generalized Stirling_2 Triangle k = -4 | ||||

Sum: A049119 | all partitions: A134149 | ~ by length: A035469 | ~ by biggest part: A157398 | diagonal: A007559 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

5 | [1,4] | [4,1] | [1,4] | 4 |

41 | [1,12,28] | [28,12,1] | [1,12,28] | 28 |

465 | [1,24,48,112,280] | [280,160,24,1] | [1,72,112,280] | 280 |

6721 | [1,40,240,280,1120,1400,3640] | [3640,2520,520,40,1] | [1,280,1400,1400,3640] | 3640 |

Generalized Stirling_2 Triangle k = -3 | ||||

Sum: A049118 | all partitions: A134144 | ~ by length: A035342 | ~ by biggest part: A157399 | diagonal: A001147 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

4 | [1,3] | [3,1] | [1,3] | 3 |

25 | [1,9,15] | [15,9,1] | [1,9,15] | 15 |

211 | [1,18,27,60,105] | [105,87,18,1] | [1,45,60,105] | 105 |

2236 | [1,30,135,150,450,525,945] | [945,975,285,30,1] | [1,165,600,525,945] | 945 |

Generalized Stirling_2 Triangle k = -2 | ||||

Sum: A000262 | all partitions: A130561 | ~ by length: A105278 | ~ by biggest part: A157400 | diagonal: A000142 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

3 | [1,2] | [2,1] | [1,2] | 2 |

13 | [1,6,6] | [6,6,1] | [1,6,6] | 6 |

73 | [1,12,12,24,24] | [24,36,12,1] | [1,24,24,24] | 24 |

501 | [1,20,60,60,120,120,120] | [120,240,120,20,1] | [1,80,180,120,120] | 120 |

Generalized Stirling_2 Triangle k = -1 | ||||

Sum: A000110 | all partitions: A036040 | ~ by length: A008277 | ~ by biggest part: A080510 | diagonal: A000012 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

2 | [1,1] | [1,1] | [1,1] | 1 |

5 | [1,3,1] | [1,3,1] | [1,3,1] | 1 |

15 | [1,6,3,4,1] | [1,7,6,1] | [1,9,4,1] | 1 |

52 | [1,10,15,10,10,5,1] | [1,15,25,10,1] | [1,25,20,5,1] | 1 |

Generalized Stirling_2 Triangle k = 0 | ||||

Sum: A000012 | all partitions: A155972 | ~ by length: A023531 | ~ by biggest part: A000000 | diagonal: A000000 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

1 | [1,0] | [0,1] | [1,0] | 0 |

1 | [1,0,0] | [0,0,1] | [1,0,0] | 0 |

1 | [1,0,0,0,0] | [0,0,0,1] | [1,0,0,0] | 0 |

1 | [1,0,0,0,0,0,0] | [0,0,0,0,1] | [1,0,0,0,0] | 0 |

Generalized Stirling_2 Triangle k = 1 | ||||

Sum: A001515 | all partitions: A143171 | ~ by length: A001497 | ~ by biggest part: A157401 | diagonal: A001147 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

2 | [1,1] | [1,1] | [1,1] | 1 |

7 | [1,3,3] | [3,3,1] | [1,3,3] | 3 |

37 | [1,6,3,12,15] | [15,15,6,1] | [1,9,12,15] | 15 |

266 | [1,10,15,30,30,75,105] | [105,105,45,10,1] | [1,25,60,75,105] | 105 |

Generalized Stirling_2 Triangle k = 2 | ||||

Sum: A015735 | all partitions: A143172 | ~ by length: A004747 | ~ by biggest part: A157402 | diagonal: A008544 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

3 | [1,2] | [2,1] | [1,2] | 2 |

17 | [1,6,10] | [10,6,1] | [1,6,10] | 10 |

145 | [1,12,12,40,80] | [80,52,12,1] | [1,24,40,80] | 80 |

1661 | [1,20,60,100,200,400,880] | [880,600,160,20,1] | [1,80,300,400,880] | 880 |

Generalized Stirling_2 Triangle k = 3 | ||||

Sum: A016036 | all partitions: A143173 | ~ by length: A000369 | ~ by biggest part: A157403 | diagonal: A008545 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

4 | [1,3] | [3,1] | [1,3] | 3 |

31 | [1,9,21] | [21,9,1] | [1,9,21] | 21 |

361 | [1,18,27,84,231] | [231,111,18,1] | [1,45,84,231] | 231 |

5626 | [1,30,135,210,630,1155,3465] | [3465,1785,345,30,1] | [1,165,840,1155,3465] | 3465 |

Generalized Stirling_2 Triangle k = 4 | ||||

Sum: A028575 | all partitions: A144267 | ~ by length: A011801 | ~ by biggest part: A157404 | diagonal: A008546 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

5 | [1,4] | [4,1] | [1,4] | 4 |

49 | [1,12,36] | [36,12,1] | [1,12,36] | 36 |

721 | [1,24,48,144,504] | [504,192,24,1] | [1,72,144,504] | 504 |

14177 | [1,40,240,360,1440,2520,9576] | [9576,3960,600,40,1] | [1,280,1800,2520,9576] | 9576 |

Generalized Stirling_2 Triangle k = 5 | ||||

Sum: A028844 | all partitions: A144268 | ~ by length: A013988 | ~ by biggest part: A157405 | diagonal: A008543 |

1 | [1] | [1] | [1] | 1 |

1 | [1] | [1] | [1] | 1 |

6 | [1,5] | [5,1] | [1,5] | 5 |

71 | [1,15,55] | [55,15,1] | [1,15,55] | 55 |

1261 | [1,30,75,220,935] | [935,295,30,1] | [1,105,220,935] | 935 |

29906 | [1,50,375,550,2750,4675,21505] | [21505,7425,925,50,1] | [1,425,3300,4675,21505] | 21505 |

Note: If no exact match could be found a reference was given which contains useful hints and links related to the sequence.