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A306081 Expansion of e.g.f. Product_{k>=1} ((1 + (exp(x) - 1)^k) / (1 - (exp(x) - 1)^k))^k. 4
1, 2, 14, 134, 1574, 22262, 367814, 6907574, 144942854, 3357588662, 85000841414, 2331998188214, 68862337593734, 2176283210561462, 73250933670041414, 2614843434740912054, 98632371931151518214, 3918608865052986708662, 163507638190268814991814 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Convolution of A306080 and A306046.
LINKS
FORMULA
a(n) = Sum_{k=0..n} Stirling2(n,k) * A156616(k) * k!.
a(n) ~ n! * exp(3 * (7*Zeta(3))^(1/3) * n^(2/3) / (4 * log(2)^(2/3)) + (1 - log(2)) * (7*Zeta(3))^(2/3) * n^(1/3) / (8 * log(2)^(4/3)) - 7*(log(2)^2 + log(2) - 1) * Zeta(3) / (48 * log(2)^2) + 1/12) * (7*Zeta(3))^(7/36) / (A * 2^(13/12) * sqrt(3*Pi) * n^(25/36) * (log(2))^(n + 11/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jun 22 2018
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[((1 + (Exp[x] - 1)^k)/(1 - (Exp[x] - 1)^k))^k, {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!
CROSSREFS
Sequence in context: A157085 A073553 A144097 * A326886 A111424 A317356
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jun 20 2018
STATUS
approved

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Last modified March 28 13:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)