A347949 E.g.f.: 1 / (1 - Sum_{k>=1} x^prime(k) / prime(k)).

1, 0, 1, 2, 6, 64, 170, 2988, 14616, 180192, 1934712, 21673200, 300266736, 4220710272, 61785461712, 1003589762784, 17448621367680, 327598207658496, 6279739240655232, 134169095009652480, 2817563310900129024, 64570676279407718400, 1547773850801172960000, 38824156236466815920640

Offset: 0

Author

Ilya Gutkovskiy, Sep 20 2021

Keywords

• nonn

Crossrefs

Cf. A007840, A010051, A023360, A218002, A347948.

Programs

Mathematica

nmax = 23; CoefficientList[Series[1/(1 - Sum[x^Prime[k]/Prime[k], {k, 1, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (k - 1)! Boole[PrimeQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * (k-1)! * A010051(k) * a(n-k).