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A333985 a(0) = 0; a(n) = 6^(n-1) + (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * 6^(k-1) * (n-k) * a(n-k). 4
0, 1, 8, 102, 2448, 99576, 6070032, 517803840, 58901955840, 8614609282944, 1574889814326528, 351896788824053760, 94354291010501932032, 29899137879209196380160, 11053567519385396409446400, 4715135497874174650128617472, 2298676381054790419739595571200, 1270045124912998373344157769891840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

Sum_{n>=0} a(n) * x^n / (n!)^2 = -log((7 - BesselI(0,2*sqrt(6*x))) / 6).

MATHEMATICA

a[0] = 0; a[n_] := a[n] = 6^(n - 1) + (1/n) Sum[Binomial[n, k]^2 6^(k - 1) (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]

nmax = 17; CoefficientList[Series[-Log[(7 - BesselI[0, 2 Sqrt[6 x]])/6], {x, 0, nmax}], x] Range[0, nmax]!^2

CROSSREFS

Cf. A102223, A333981, A333982, A333983, A333984, A337597.

Sequence in context: A001575 A328061 A305603 * A297069 A090237 A222664

Adjacent sequences:  A333982 A333983 A333984 * A333986 A333987 A333988

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 04 2020

STATUS

approved

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Last modified January 23 07:43 EST 2022. Contains 350509 sequences. (Running on oeis4.)