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%I #8 Feb 02 2021 23:23:36
%S 1,1,10,255,12196,939155,106161756,16554165495,3404986723720,
%T 893137635015219,290965846152033460,115256679181251696803,
%U 54552992572663333862400,30406695393635479756804525,19712738332895648545008815416,14707436666152282009334357074335
%N a(n) = (n!)^2 * [x^n] 1 / BesselJ(0,2*sqrt(x))^n.
%H Alois P. Heinz, <a href="/A336665/b336665.txt">Table of n, a(n) for n = 0..99</a>
%t Table[(n!)^2 SeriesCoefficient[1/BesselJ[0, 2 Sqrt[x]]^n, {x, 0, n}], {n, 0, 15}]
%t 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}]
%Y Cf. A000275, A033935, A336271, A336638, A336639.
%Y Main diagonal of A340986.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jul 29 2020
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