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A306082
Expansion of e.g.f. Product_{k>=1} 1/(1 - (exp(x) - 1)^(k^2)).
3
1, 1, 3, 13, 99, 901, 8763, 92653, 1125939, 16333141, 274594923, 5041348093, 97841114979, 2007694705381, 44043941312283, 1036207737976333, 25969433606691219, 688418684249653621, 19275116061819888843, 571069469474068377373, 17898523203378840958659
OFFSET
0,3
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * A001156(k) * k!.
a(n) ~ n! * exp(3 * 2^(-5/3) * Zeta(3/2)^(2/3) * (Pi*n/log(2))^(1/3)) * Zeta(3/2)^(2/3) / (2^(13/6) * sqrt(3) * Pi^(7/6) * n^(7/6) * (log(2))^(n - 1/6)).
MAPLE
a:=series(mul(1/(1-(exp(x)-1)^(k^2)), k=1..100), x=0, 21): seq(n!*coeff(a, x, n), n=0..20); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - (Exp[x] - 1)^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 20 2018
STATUS
approved