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T03

T_{3}(n,k) = \zeta(k - n, 1) - \zeta(k - n, k + 1)

TriangleForm
0  
0 1  
0 1 2  
0 1 3 3  
0 1 5 6 4  
0 1 9 14 10 5  
0 1 17 36 30 15 6
sum als gcd lcm
0 0 0 1
1 1 0 1
3 1 2 2
7 1 3 3
16 2 1 60
39 1 1 630
105 1 1 3060
RectangleForm
0 0 0 0 0 0 0
1 1 1 1 1 1 1
2 3 5 9 17 33 65
3 6 14 36 98 276 794
4 10 30 100 354 1300 4890
5 15 55 225 979 4425 20515
6 21 91 441 2275 12201 67171
Fingerprint
SubSeqType 0 1 2 3
Row A000004 A000012 A000051 A001550
Column A001477 A000217 A000330 A000537
DiagRow A031971 A076015 A000000 A000000
DiagColumn A031971 A121706 A000000 A000000
Characteristic SUM ALS LCM GCD
Sequence A103439 A000000 A000000 A000000

Maple T3 := proc(n, k) Zeta(0, k − n, 1) − Zeta(0, k − n, k + 1) end:

TeX T_{3}(n,k) = \zeta(k - n, 1) - \zeta(k - n, k + 1)