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T10

T_{10}(n,k)=\frac{2k+1}{n+k+1}\binom{2n}{n-k}

TriangleForm
1  
1 1  
2 3 1  
5 9 5 1  
14 28 20 7 1  
42 90 75 35 9 1  
132 297 275 154 54 11 1
sum als gcd lcm
1 1 0 1
2 0 0 1
6 0 1 6
20 0 1 45
70 0 1 140
252 0 1 3150
924 0 1 207900
RectangleForm
1 1 2 5 14 42 132
1 3 9 28 90 297 1001
1 5 20 75 275 1001 3640
1 7 35 154 637 2548 9996
1 9 54 273 1260 5508 23256
1 11 77 440 2244 10659 48279
1 13 104 663 3705 19019 92092
Fingerprint
SubSeqType 0 1 2 3
Row A000108 A000245 A000344 A000588
Column A000012 A005408 A014107 A000000
DiagRow A126596 A000000 A000000 A000000
DiagColumn A126596 A000000 A000000 A000000
Characteristic SUM ALS LCM GCD
Sequence A000984 A000007 A000000 A000000

Maple T10 := proc(n, k) (2*k+1)*binomial(2*n, n−k)/(n+k+1) end:

TeX T_{10}(n,k)=\frac{2k+1}{n+k+1}\binom{2n}{n-k}