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A336665 a(n) = (n!)^2 * [x^n] 1 / BesselJ(0,2*sqrt(x))^n. 3
1, 1, 10, 255, 12196, 939155, 106161756, 16554165495, 3404986723720, 893137635015219, 290965846152033460, 115256679181251696803, 54552992572663333862400, 30406695393635479756804525, 19712738332895648545008815416, 14707436666152282009334357074335 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

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}]

CROSSREFS

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

Main diagonal of A340986.

Sequence in context: A100743 A251588 A126468 * A024293 A120268 A001824

Adjacent sequences: A336662 A336663 A336664 * A336666 A336667 A336668

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 29 2020

STATUS

approved

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Last modified December 3 08:35 EST 2022. Contains 358515 sequences. (Running on oeis4.)