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T15

T_{15}(n,k)= \genfrac{\{}{.}{0pt}{}{d_n =\text{denom}(B_{n+1}(z+1)-B_{n+1}(1))}{[x^k] d_n \sum_{j=0}^{n}\binom{n+1}{j+1}B_{n-j}(1)(x-1)^j}

TriangleForm
1  
0 1  
0 -1 2  
0 0 -1 1  
0 1 1 -9 6  
0 0 1 1 -4 2  
0 -1 -1 6 6 -15 6
sum als gcd lcm
1 1 0 1
1 1 0 1
3 1 1 2
2 0 1 1
17 3 3 18
8 2 2 4
35 9 1 30
RectangleForm
1 0 0 0 0 0 0
1 -1 0 1 0 -1 0
2 -1 1 1 -1 -2 3
1 -9 1 6 -2 -17 3
6 -4 6 5 -17 -7 28
2 -15 5 25 -7 -38 23
6 -9 25 7 -38 -21 5150
Fingerprint
SubSeqType 0 1 2 3
Row A000007 A050925 A000000 A000000
Column A000000 A000000 A000000 A000000
DiagRow A000000 A000000 A000000 A000000
DiagColumn A000000 A000000 A000000 A000000
Characteristic SUM ALS LCM GCD
Sequence A000000 A000000 A000000 A000000

Maple T15 := proc(n,k) local j; coeff(denom(B(n+1,y+1)-B(n+1,1))*add(binomial(n+1,j+1)* B(n-j,1)*(x-1)^j,j=0..n),x,k) end:

TeX T_{15}(n,k)= \genfrac{\{}{.}{0pt}{}{d_n =\text{denom}(B_{n+1}(z+1)-B_{n+1}(1))}{[x^k] d_n \sum_{j=0}^{n}\binom{n+1}{j+1}B_{n-j}(1)(x-1)^j}