A320288 a(n) = n! * [x^n] exp(exp(x)*(exp(n*x) - 1)/(exp(x) - 1) - n).

1, 1, 14, 504, 35054, 4004100, 680823583, 161337142848, 50830272555828, 20549783554154775, 10370522690234157175, 6390016526512315766520, 4721172172018812127424546, 4119920939845363203406535407, 4192465334819134111336349480680, 4920767556196547768620408273728000

Offset: 0

Author

Ilya Gutkovskiy, Oct 09 2018

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..218

Crossrefs

Cf. A103438, A319508.

Programs

Mathematica

Table[n! SeriesCoefficient[Exp[Exp[x] (Exp[n x] - 1)/(Exp[x] - 1) - n], {x, 0, n}], {n, 0, 15}]

PARI

a(n)={my(A=O(x^(n+2))); n!*polcoef((exp(exp(x + A)*(exp(n*x + A) - 1)/(exp(x + A) - 1) - n)), n)}; \\ Andrew Howroyd, Nov 04 2018

Formula

a(n) = n! * [x^n] exp(exp(x) + exp(2*x) + exp(3*x) + ... + exp(n*x) - n).

a(n) ~ c * exp(n*exp(1) - 3*n) * n^(2*n), where c = exp((exp(1) - 1)/2) / sqrt(exp(1) - 1) = 1.801245710492990660565773944914841332489711300610532... - Vaclav Kotesovec, Jul 02 2022, updated Mar 18 2024