A353162 Expansion of e.g.f. exp(Sum_{p prime} p * x^p).

1, 0, 4, 18, 48, 1320, 4200, 115920, 994560, 11793600, 264055680, 2601244800, 67761429120, 1067726499840, 21513457405440, 485310649824000, 9925206939648000, 254012624170905600, 6174538264806912000, 160933619800835481600, 4458470291543671603200

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{p<=n, p prime} p^2 * a(n-p)/(n-p)!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, isprime(k)*k*x^k))))
(PARI) a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, isprime(k)*k^2*a(n-k)/(n-k)!));

Crossrefs

Cf. A000040, A082579, A218002, A351940, A353163, A353164.

Sequence in context: A081528 A056147 A181857 * A303737 A180805 A120656

Adjacent sequences: A353159 A353160 A353161 * A353163 A353164 A353165

Keyword

nonn

Author

Seiichi Manyama, Apr 28 2022

Status

approved