A335848 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * k!! * a(n-k).

1, 1, 4, 21, 152, 1355, 14568, 182427, 2612224, 42073209, 752981280, 14823367845, 318347145216, 7406554353939, 185573713100160, 4981725842622795, 142650055922872320, 4340032650657965745, 139809806502181765632, 4754045863586538697077, 170163141506896128122880

Offset: 0

Author

Ilya Gutkovskiy, Jun 26 2020

Keywords

• nonn

Crossrefs

Cf. A002866, A006882, A292778, A308939.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] k!! a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
nmax = 20; CoefficientList[Series[1/(1 - x Exp[x^2/2] (1 + Sqrt[Pi/2] Erf[x/Sqrt[2]])), {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: 1 / (1 - x * exp(x^2/2) * (1 + sqrt(Pi/2) * erf(x/sqrt(2)))), where erf() is the error function.