A352004 Expansion of e.g.f. Product_{k>=1} 1/(1 - x^prime(k))^(1/prime(k)!).

1, 0, 1, 1, 9, 11, 295, 337, 13041, 45550, 1043211, 3359786, 150500053, 440947300, 23238057921, 145733451241, 5097210717873, 29028404123105, 1710073810205317, 8663532297784519, 574604164708374861, 5108822296820280256, 246335435270285805885

Offset

0,5

Links

Table of n, a(n) for n=0..22.

Formula

E.g.f.: exp( Sum_{k>=1} A352012(k)*x^k/k! ) where A352012(k) = Sum_{p|k, p prime} (k-1)!/(p-1)!.

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/prod(k=1, N, (1-x^k)^(isprime(k)/k!))))
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=1, N, sumdiv(k, d, isprime(d)*(k-1)!/(d-1)!)*x^k/k!))))

Crossrefs

Cf. A209902, A318913, A352012.

Sequence in context: A146366 A146603 A159003 * A196509 A269026 A124606

Adjacent sequences: A352001 A352002 A352003 * A352005 A352006 A352007

Keyword

nonn

Author

Seiichi Manyama, Feb 28 2022

Status

approved