A306147 Expansion of e.g.f. Product_{k>=1} (1 + (exp(x)-1)^(k^2)) / (1 - (exp(x)-1)^(k^2)).

1, 2, 6, 26, 198, 2042, 22566, 259226, 3249798, 47156282, 799108326, 15116875226, 305203728198, 6488119430522, 146602455461286, 3557921474016026, 92563621667899398, 2554423824661976762, 74142584637465337446, 2258422219660738881626, 72255096004023644467398

Offset

0,2

Comments

Convolution of A306082 and A306083.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..420

Formula

a(n) = Sum_{k=0..n} Stirling2(n,k) * A103265(k) * k!.

a(n) ~ n! * ((2*sqrt(2) - 1) * Zeta(3/2))^(2/3) * exp(3 * (Pi/log(2))^(1/3) * ((2*sqrt(2) - 1) * Zeta(3/2))^(2/3) * n^(1/3) / 4) / (8 * sqrt(3) * Pi^(7/6) * n^(7/6) * (log(2))^(n - 1/6)).

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + (Exp[x] - 1)^(k^2)) / (1 - (Exp[x] - 1)^(k^2)), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!

Crossrefs

Cf. A001156, A033461, A103265, A306082, A306083.

Sequence in context: A032014 A112948 A007139 * A331937 A162438 A137071

Adjacent sequences: A306144 A306145 A306146 * A306148 A306149 A306150

Keyword

nonn

Author

Vaclav Kotesovec, Jun 23 2018

Status

approved