A336947 E.g.f.: 1 / (exp(-2*x) - x).

1, 3, 14, 98, 920, 10792, 151888, 2494032, 46803072, 988095104, 23178247424, 598074306304, 16835199087616, 513385352524800, 16859837094942720, 593234633904293888, 22265289445252628480, 887889931920920313856, 37489832605652634763264, 1670894259596134872711168

Offset: 0

Author

Ilya Gutkovskiy, Aug 08 2020

Keywords

• nonn

Crossrefs

Cf. A072597, A216794, A336948, A336949, A336950.

Programs

Mathematica

nmax = 19; CoefficientList[Series[1/(Exp[-2 x] - x), {x, 0, nmax}], x] Range[0, nmax]!
Table[n! Sum[(2 (n - k + 1))^k/k!, {k, 0, n}], {n, 0, 19}]
a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] - Sum[Binomial[n, k] (-2)^k a[n - k], {k, 2, n}]; Table[a[n], {n, 0, 19}]

PARI

seq(n)={ Vec(serlaplace(1 / (exp(-2*x + O(x*x^n)) - x))) } \\ Andrew Howroyd, Aug 08 2020

Formula

a(n) = n! * Sum_{k=0..n} (2 * (n-k+1))^k / k!.

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

a(n) ~ n! / ((1 + LambertW(2)) * (LambertW(2)/2)^(n+1)). - Vaclav Kotesovec, Aug 09 2021