A337592 - OEIS

A337592

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

1, 1, 4, 28, 312, 4936, 104128, 2806336, 93560064, 3765265408, 179415074304, 9964625629696, 636737424291840, 46303081167540224, 3796275000959266816, 348100339275620651008, 35448445862069986361344, 3984266642444252234153984, 491556877841462376382332928

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..18.

FORMULA

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

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

MATHEMATICA

a[0] = 1; a[n_] := a[n] = (1/n) Sum[Binomial[n, k]^2 k 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]

nmax = 18; CoefficientList[Series[Exp[(BesselI[0, 2 Sqrt[2 x]] - 1)/2], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS