A333984 - OEIS

A333984

a(0) = 0; a(n) = 5^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 5^(k-1) * (n-k) * a(n-k).

0, 1, 7, 82, 1839, 69630, 3950650, 313747050, 33224570175, 4523562983350, 769859662962750, 160137417877796250, 39971947204607486250, 11791483690935887486250, 4058152793413483423916250, 1611522009185095020022068750, 731368135285580087866788609375, 376178084508304435598172207843750

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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((6 - BesselI(0,2*sqrt(5*x))) / 5).

MATHEMATICA

a[0] = 0; a[n_] := a[n] = 5^(n - 1) + (1/n) Sum[Binomial[n, k]^2 5^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]

nmax = 17; CoefficientList[Series[-Log[(6 - BesselI[0, 2 Sqrt[5 x]])/5], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A102223, A333981, A333982, A333983, A333985, A337595.