A339014 E.g.f.: exp(2 * (exp(x) - 1 - x - x^2 / 2)).

1, 0, 0, 2, 2, 2, 42, 142, 366, 3082, 18626, 86990, 596158, 4485626, 30214498, 224897662, 1871664190, 15587540042, 134045407458, 1231183979886, 11725017784574, 114812031304986, 1170100796863202, 12371771640238174, 134796972965052350, 1514854948728869354

Offset: 0

Author

Ilya Gutkovskiy, Nov 19 2020

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..563

Crossrefs

Cf. A001861, A006505, A194689.

Programs

Mathematica

nmax = 25; CoefficientList[Series[Exp[2 (Exp[x] - 1 - x - x^2/2)], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n - 1, k - 1] a[n - k], {k, 3, n}]; Table[a[n], {n, 0, 25}]

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(2 * (exp(x) - 1 - x - x^2/2)))) \\ Michel Marcus, Nov 19 2020

Formula

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

a(n) = Sum_{k=0..n} binomial(n,k) * A006505(k) * A006505(n-k).