A353163 Expansion of e.g.f. exp(Sum_{p prime} x^p / (p-1)!).

1, 0, 2, 3, 12, 65, 210, 1477, 7560, 45864, 338310, 2176031, 17657640, 139280869, 1150004856, 10572694860, 94834041120, 931995595457, 9384294360168, 96974005210273, 1066116104926500, 11838081891521760, 137785102884102366, 1652584041236345933

Offset: 0

Author

Seiichi Manyama, Apr 28 2022

Keywords

• nonn

Crossrefs

Cf. A000040, A000248, A190476, A353162.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(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-1, k-1)*a(n-k)));

Formula

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