A347665 E.g.f.: exp( exp(x) * (1 + x + x^2 / 2) - 1 ).

1, 2, 8, 39, 227, 1518, 11368, 93796, 842416, 8158942, 84581560, 932878169, 10891741957, 134043979644, 1732583270218, 23445954950207, 331260511278659, 4874617929283392, 74548457001207068, 1182551615010825076, 19423368875596930596, 329809489306236629874

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2021

Keywords

• nonn

Comments

Exponential transform of A000124.

Crossrefs

Cf. A000085, A000124, A209801, A279361, A347666.

Programs

Mathematica

nmax = 21; CoefficientList[Series[Exp[Exp[x] (1 + x + x^2/2) - 1], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (k (k + 1)/2 + 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A000124(k) * a(n-k).