A307770 Expansion of e.g.f. 1/(1 - Sum_{k>=1} prime(k)*x^k/k!).

1, 2, 11, 89, 957, 12871, 207717, 3910931, 84155053, 2037195551, 54795228241, 1621233039941, 52328310410427, 1829742961027269, 68901415049874055, 2779901582389463177, 119635322278784511015, 5470390958849723994819, 264850557367286330886261, 13535194864326763053170325

Offset: 0

Author

Ilya Gutkovskiy, Apr 27 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..386

Crossrefs

Cf. A000040, A007446, A030017, A302191, A302192, A302194.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(
      binomial(n, j)*ithprime(j)*a(n-j), j=1..n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 24 2021

Mathematica

nmax = 19; CoefficientList[Series[1/(1 - Sum[Prime[k] x^k/k!, {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!