A336948 E.g.f.: 1 / (exp(-3*x) - x).

1, 4, 23, 195, 2229, 31863, 546255, 10925757, 249753897, 6422808411, 183524701779, 5768419379913, 197791542799965, 7347180526444359, 293912722687075767, 12597352573293062757, 575928946256877156177, 27976119070974574461363, 1438896686251112024068251

Offset: 0

Author

Ilya Gutkovskiy, Aug 08 2020

Keywords

• nonn

Crossrefs

Cf. A072597, A328182, A336947, A336949, A336951.

Programs

Mathematica

nmax = 18; CoefficientList[Series[1/(Exp[-3 x] - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(3 (n - k + 1))^k/k!, {k, 0, n}], {n, 0, 18}]
a[0] = 1; a[n_] := a[n] = 4 n a[n - 1] - Sum[Binomial[n, k] (-3)^k a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 18}]

PARI

seq(n)={ Vec(serlaplace(1 / (exp(-3*x + O(x*x^n)) - x))) } \\ Andrew Howroyd, Aug 08 2020

Formula

a(n) = n! * Sum_{k=0..n} (3 * (n-k+1))^k / k!.

a(0) = 1; a(n) = 4 * n * a(n-1) - Sum_{k=2..n} binomial(n,k) * (-3)^k * a(n-k).

a(n) ~ n! / ((1 + LambertW(3)) * (LambertW(3)/3)^(n+1)). - Vaclav Kotesovec, Aug 09 2021