A326886 E.g.f.: Product_{k>=1} (1 + k*(exp(x)-1)^k) / (1 - k*(exp(x)-1)^k).

1, 2, 14, 134, 1574, 22262, 370694, 7008374, 147805574, 3447703862, 88047037574, 2438080410614, 72703788119174, 2321967591003062, 79030014919422854, 2854499200663284854, 109018338380110506374, 4388176453133542327862, 185612789014681549094534

Offset

0,2

Links

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

Formula

a(n) = Sum_{k=0..n} A265758(k)*Stirling2(n,k)*k!.

a(n) ~ c * 2 * (3^(2/3) + 2) * n! / (3*(3^(2/3) - 2) * (3^(1/3) - 1) * log(1 + 3^(-1/3))^(n+1)), where c = Product_{k>=4} (1 + k/3^(k/3)) / (1 - k/3^(k/3)) = 153073.83255100475812062139772279157814388739...

Mathematica

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

Crossrefs

Cf. A265758, A306045, A326884, A326885, A326887.

Sequence in context: A073553 A144097 A306081 * A111424 A317356 A375507

Adjacent sequences: A326883 A326884 A326885 * A326887 A326888 A326889

Keyword

nonn

Author

Vaclav Kotesovec, Jul 31 2019

Status

approved