A336609 Sum_{n>=0} a(n) * x^n / (n!)^2 = exp(1 / BesselJ(0,2*sqrt(x)) - 1).

1, 1, 5, 52, 917, 24396, 909002, 45062697, 2862532213, 226403027044, 21794813189810, 2507115921526437, 339421509956163362, 53393907140415300317, 9653668439939308357991, 1987242385193691443059527, 461955240782446199029195253

Offset

0,3

Links

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

Formula

a(0) = 1; a(n) = (1/n) * Sum_{k=1..n} binomial(n,k)^2 * k * A000275(k) * a(n-k).

Mathematica

nmax = 16; CoefficientList[Series[Exp[1/BesselJ[0, 2 Sqrt[x]] - 1], {x, 0, nmax}], x] Range[0, nmax]!^2
A000275[0] = 1; A000275[n_] := A000275[n] = -Sum[(-1)^(n - k) Binomial[n, k]^2 A000275[k], {k, 0, n - 1}]; a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k A000275[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]

Crossrefs

Cf. A000275, A002190, A023998.

Sequence in context: A076281 A099977 A274257 * A303000 A278879 A322195

Adjacent sequences: A336606 A336607 A336608 * A336610 A336611 A336612

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 27 2020

Status

approved