A336665 a(n) = (n!)^2 * [x^n] 1 / BesselJ(0,2*sqrt(x))^n.

1, 1, 10, 255, 12196, 939155, 106161756, 16554165495, 3404986723720, 893137635015219, 290965846152033460, 115256679181251696803, 54552992572663333862400, 30406695393635479756804525, 19712738332895648545008815416, 14707436666152282009334357074335

Offset: 0

Author

Ilya Gutkovskiy, Jul 29 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..99

Crossrefs

Cf. A000275, A033935, A336271, A336638, A336639.

Main diagonal of A340986.

Programs

Mathematica

Table[(n!)^2 SeriesCoefficient[1/BesselJ[0, 2 Sqrt[x]]^n, {x, 0, n}], {n, 0, 15}]
A287316[n_, k_] := A287316[n, k] = If[n == 0, 1, If[k < 1, 0, Sum[Binomial[n, j]^2 A287316[n - j, k - 1], {j, 0, n}]]]; b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[(-1)^(j + 1) Binomial[n, j]^2 A287316[j, k] b[n - j, k], {j, 1, n}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 15}]

Formula

a(n) ~ c * d^n * n!^2 / sqrt(n), where d = 3.431031961004073074179854315227049823720211... and c = 0.31156343453490677011135864540173577785263... - Vaclav Kotesovec, May 04 2024