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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

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...

Mathematica

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

Crossrefs

Cf. A006906, A167137, A305986, A326884.

Sequence in context: A355409 A112243 A083836 * A159313 A318580 A054910

Adjacent sequences: A326882 A326883 A326884 * A326886 A326887 A326888

Keyword

nonn

Author

Vaclav Kotesovec, Jul 31 2019

Status

approved