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

0,3

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

(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)));

Crossrefs

Cf. A000040, A000248, A190476, A353162.

Sequence in context: A188588 A032133 A155579 * A108261 A013152 A012911

Adjacent sequences: A353160 A353161 A353162 * A353164 A353165 A353166

Keyword

nonn

Author

Seiichi Manyama, Apr 28 2022

Status

approved