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
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..400
Programs
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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]!
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...