A343686 a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * (n-k-1)! * a(k).

1, 4, 33, 410, 6796, 140824, 3501782, 101589732, 3368237928, 125634319104, 5206805098752, 237370661584704, 11805144854303760, 636030155604374400, 36903603627294958416, 2294156656214759133024, 152126925169297299197184, 10718105879980375520103936, 799564645068022035991527552

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: 1 / (1 - 3*x + log(1 - x)).

a(n) ~ n! / ((3/c + 2 - c) * (1 - c/3)^n), where c = LambertW(3*exp(2)) = 2.2761339297716461777892556270138... - Vaclav Kotesovec, Apr 26 2021

Mathematica

a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] + Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[1/(1 - 3 x + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A007840, A052820, A053486, A343685, A343687.

Sequence in context: A370930 A213641 A343673 * A364980 A360234 A111534

Adjacent sequences: A343683 A343684 A343685 * A343687 A343688 A343689

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 26 2021

Status

approved