A353165 Expansion of e.g.f. 1/(1 - Sum_{p prime} x^p / (p-1)!).

1, 0, 2, 3, 24, 125, 900, 7987, 72240, 817488, 9536940, 127816931, 1830739680, 28597812685, 481145656992, 8650951895040, 166376275228800, 3392537585542577, 73342277086465296, 1672523286398099407, 40158685461798481560, 1012415090497566344400

Offset: 0

Author

Seiichi Manyama, Apr 28 2022

Keywords

• nonn

Crossrefs

Cf. A000040, A006153, A347948, A353163, A353164.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, isprime(k)*x^k/(k-1)!))))

PARI

a(n) = if(n==0, 1, sum(k=1, n, isprime(k)*k*binomial(n, k)*a(n-k)));

Formula

a(0) = 1; a(n) = Sum_{p<=n, p prime} p * binomial(n,p) * a(n-p).