A326885 E.g.f.: Product_{k>=1} 1/(1 - k*(exp(x)-1)^k).
1, 1, 7, 55, 595, 7351, 110587, 1884415, 36154195, 771983911, 18141124267, 463345240975, 12792709110595, 379854657215671, 12057296962232347, 407072488594360735, 14565548824196479795, 550582832110097346631, 21917855760706255154827, 916261422041320023467695
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..400
Programs
-
Mathematica
nmax = 20; CoefficientList[Series[Product[1/(1-k*(Exp[x]-1)^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
Formula
a(n) = Sum_{k=0..n} A006906(k)*Stirling2(n,k)*k!.
a(n) ~ c * n! / ((3^(2/3) - 2) * (3^(2/3) - 1) * log(1 + 3^(-1/3))^(n+1)), where c = Product_{k>=4} 1/(1 - k/3^(k/3)) = 3468.14377687388560106742710672518465524...