OFFSET
0,19
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.
Peter Luschny, Illustrating the polynomials.
EXAMPLE
[0] [1]
[1] [0, 1]
[2] [0, 0, 1]
[3] [0, 0, 1, 1]
[4] [0, 0, 1, 1, 1]
[5] [0, 0, 1, 3, 1, 1]
[6] [0, 0, 1, 1, 17, 1, 1]
[7] [0, 0, 691, 691, 59, 41, 5, 1]
[8] [0, 0, 14, 2, 359, 8, 4, 1, 1]
[9] [0, 0, 3617, 10851, 1237, 217, 293, 1, 7, 1]
MATHEMATICA
A368846[n_, k_]:=If[k==0, Boole[n==0], (-1)^(n+k)2Binomial[2k-1, n]Binomial[2n+1, 2k]];
Numerator[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].numerator() for k in range(n+1)])
CROSSREFS
KEYWORD
AUTHOR
Peter Luschny, Jan 07 2024
STATUS
approved