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A306045
Expansion of e.g.f. Product_{k>=1} (1 + (exp(x) - 1)^k) / (1 - (exp(x) - 1)^k).
9
1, 2, 10, 74, 682, 7562, 98410, 1463114, 24367402, 449039882, 9069093610, 199050295754, 4713774570922, 119735740542602, 3246094020405610, 93519923311825994, 2852458136048627242, 91805618091515859722, 3108657616523130770410, 110453876295411957125834
OFFSET
0,2
COMMENTS
Convolution of A167137 and A305550.
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * A015128(k) * k!.
a(n) ~ n! * exp(Pi^2 * (1 - log(2)) / (16*log(2)) + Pi * sqrt(n/(2*log(2)))) / (8*n*(log(2))^n).
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[(1 + (Exp[x] - 1)^k) / (1 - (Exp[x] - 1)^k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 18 2018
STATUS
approved