A346430 E.g.f.: 1 / (1 - x - Sum_{k>=2} prime(k-1) * x^k / k!).

1, 1, 4, 21, 149, 1317, 13985, 173207, 2451807, 39043963, 690844441, 13446183857, 285500221447, 6567135007015, 162678487750465, 4317650962178897, 122234460353464081, 3676789159574231397, 117102826395968235853, 3936834192059910096205, 139316727760914366716635

Offset: 0

Author

Ilya Gutkovskiy, Aug 04 2021

Keywords

• nonn

Crossrefs

Cf. A000040, A008578, A030017, A300632, A300662, A302194, A346791.

Programs

Mathematica

nmax = 20; CoefficientList[Series[1/(1 - x - Sum[Prime[k - 1] x^k/k!, {k, 2, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A008578(k) * a(n-k).