A333983 - OEIS

A333983

a(0) = 0; a(n) = 4^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 4^(k-1) * (n-k) * a(n-k).

0, 1, 6, 64, 1328, 46336, 2423040, 177379840, 17314109440, 2172895068160, 340868882825216, 65356107645583360, 15037174515952517120, 4088810357694136320000, 1297103066111891262668800, 474788193071044243776077824, 198617395218460028950533898240, 94165608216423156721014443868160

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..17.

FORMULA

Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((5 - BesselI(0,4*sqrt(x))) / 4).

MATHEMATICA

a[0] = 0; a[n_] := a[n] = 4^(n - 1) + (1/n) Sum[Binomial[n, k]^2 4^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]

nmax = 17; CoefficientList[Series[-Log[(5 - BesselI[0, 4 Sqrt[x]])/4], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A102223, A201368, A333981, A333982, A333984, A333985, A337594.