A353166 Expansion of e.g.f. exp(Sum_{k>=1} prime(k)*x^k/k).
1, 2, 7, 36, 237, 1926, 18147, 195432, 2353881, 31392522, 459730431, 7306628652, 125360110917, 2306819281806, 45287505051867, 944784879298416, 20866852729885617, 486315480759519762, 11921919558334283511, 306644867097382161972, 8255584865932073325981
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, prime(k)*x^k/k)))) -
PARI
a(n) = if(n==0, 1, (n-1)!*sum(k=1, n, prime(k)*a(n-k)/(n-k)!));
Formula
a(0) = 1; a(n) = (n-1)! * Sum_{k=1..n} prime(k) * a(n-k)/(n-k)!.