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).

0, 1, 8, 102, 2448, 99576, 6070032, 517803840, 58901955840, 8614609282944, 1574889814326528, 351896788824053760, 94354291010501932032, 29899137879209196380160, 11053567519385396409446400, 4715135497874174650128617472, 2298676381054790419739595571200, 1270045124912998373344157769891840

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: A366016 A328061 A305603 * A369184 A297069 A090237

Adjacent sequences: A333982 A333983 A333984 * A333986 A333987 A333988

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 04 2020

Status

approved