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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

%I

%S 0,1,8,102,2448,99576,6070032,517803840,58901955840,8614609282944,

%T 1574889814326528,351896788824053760,94354291010501932032,

%U 29899137879209196380160,11053567519385396409446400,4715135497874174650128617472,2298676381054790419739595571200,1270045124912998373344157769891840

%N 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).

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

%t 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}]

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

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Sep 04 2020

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Last modified May 27 02:41 EDT 2022. Contains 354093 sequences. (Running on oeis4.)