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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A167137 and A305550.

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..410

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).

MAPLE

a:=series(mul((1+(exp(x)-1)^k)/(1-(exp(x)-1)^k), k=1..100), x=0, 20): seq(n!*coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 26 2019

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

Cf. A015128, A167137, A305550, A306046.

Sequence in context: A192259 A245901 A141149 * A152408 A046863 A185971

Adjacent sequences:  A306042 A306043 A306044 * A306046 A306047 A306048

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Jun 18 2018

STATUS

approved

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Last modified June 24 17:31 EDT 2021. Contains 345417 sequences. (Running on oeis4.)