OFFSET
0,3
COMMENTS
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of the triangle, flattened).
Thomas Curtright, Scale Invariant Scattering and the Bernoulli Numbers, arXiv:2401.00586 [math-ph], Jan 2024.
EXAMPLE
Triangle starts:
[0] [1]
[1] [1, 6]
[2] [1, 1, 30]
[3] [1, 1, 60, 140]
[4] [1, 1, 45, 105, 630]
[5] [1, 1, 20, 140, 252, 2772]
[6] [1, 1, 6, 14, 1260, 693, 12012]
[7] [1, 1, 900, 2100, 945, 5940, 10296, 51480]
[8] [1, 1, 3, 1, 945, 189, 1287, 6435, 218790]
MATHEMATICA
A368846[n_, k_] := If[k==0, Boole[n==0], (-1)^(n+k) 2 Binomial[2k-1, n] Binomial[2n+1, 2k]];
Denominator[MapIndexed[Take[#, First[#2]]&, Inverse[PadRight[Table[ A368846[n, k], {n, 0, 10}, {k, 0, n}]]]]] (* Paolo Xausa, Jan 08 2024 *)
PROG
(SageMath)
M = matrix(ZZ, 10, 10, lambda n, k: A368846(n, k) if k <= n else 0)
I = M.inverse()
for n in range(9): print([I[n][k].denominator() for k in range(n+1)])
CROSSREFS
KEYWORD
AUTHOR
Peter Luschny, Jan 07 2024
STATUS
approved