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A336638

Sum_{n>=0} a(n) * x^n / (n!)^2 = 1 / BesselJ(0,2*sqrt(x))^3.

1, 3, 21, 255, 4725, 123903, 4368729, 199467243, 11455187445, 808475761695, 68805857523321, 6950458374996843, 822292004658568761, 112639503374757412875, 17688916392275574761805, 3157133540377493872350855, 635546443798928578953138165

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..16.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(k+1) * binomial(n,k)^2 * A002893(k) * a(n-k).

a(n) ~ n!^2 * n^2 / (2 * r^(n + 3/2) * BesselJ(1, 2*sqrt(r))^3), where r = BesselJZero(0,1)^2 / 4 = A115368^2/4 = 1.4457964907366961302939989396139517587... - Vaclav Kotesovec, Jul 11 2025

MATHEMATICA

nmax = 16; CoefficientList[Series[1/BesselJ[0, 2 Sqrt[x]]^3, {x, 0, nmax}], x] Range[0, nmax]!^2

a[0] = 1; a[n_] := a[n] = Sum[(-1)^(k + 1) Binomial[n, k]^2 HypergeometricPFQ[{1/2, -k, -k}, {1, 1}, 4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]

CROSSREFS

Cf. A000275, A002893, A336271, A336639.

Column k=3 of A340986.

Sequence in context: A209917 A179504 A197716 * A317059 A262939 A232470

Adjacent sequences: A336635 A336636 A336637 * A336639 A336640 A336641

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 28 2020

STATUS

approved

URL: https://oeis.org/A336638

⇱ A336638 - OEIS