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

Author

Seiichi Manyama, Feb 28 2022

Keywords

• nonn

Crossrefs

Cf. A209902, A318913, A352012.

Programs

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!))))

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)!.