A336950 E.g.f.: 1 / (1 - x * exp(2*x)).

1, 1, 6, 42, 392, 4600, 64752, 1063216, 19952256, 421227648, 9880951040, 254960721664, 7176891675648, 218857588139008, 7187394935347200, 252897556424140800, 9491754142468702208, 378509920569294684160, 15982018774576565649408, 712306819507400060502016

Offset: 0

Author

Ilya Gutkovskiy, Aug 08 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..394

Crossrefs

Column k=2 of A351790.

Cf. A001787, A006153, A122704, A216794, A235328, A336947, A336951, A336952.

Programs

Mathematica

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

PARI

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

Formula

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

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

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