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