A326887 E.g.f.: Product_{k>=1} (1 + (exp(x)-1)^k/k) / (1 - (exp(x)-1)^k/k).

1, 2, 8, 48, 364, 3320, 35464, 433692, 5962548, 90931152, 1522657264, 27765229844, 547487475484, 11604952395816, 263091290017560, 6351255101776812, 162643987129698628, 4403250400372110656, 125649232950852714496, 3769013390615951560068, 118555772298034094231724

Offset: 0

Author

Vaclav Kotesovec, Jul 31 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..420

Crossrefs

Cf. A305199, A305986, A305987.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[(1+(Exp[x]-1)^k/k)/(1-(Exp[x]-1)^k/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!

Formula

a(n) = Sum_{k=0..n} A305199(k)*Stirling2(n,k).

a(n) ~ n * (n+1)! / (16 * exp(2*gamma) * log(2)^(n+3)), where gamma is the Euler-Mascheroni constant A001620.