%I #16 Mar 18 2024 06:57:58
%S 1,1,14,504,35054,4004100,680823583,161337142848,50830272555828,
%T 20549783554154775,10370522690234157175,6390016526512315766520,
%U 4721172172018812127424546,4119920939845363203406535407,4192465334819134111336349480680,4920767556196547768620408273728000
%N a(n) = n! * [x^n] exp(exp(x)*(exp(n*x) - 1)/(exp(x) - 1) - n).
%H G. C. Greubel, <a href="/A320288/b320288.txt">Table of n, a(n) for n = 0..218</a>
%F a(n) = n! * [x^n] exp(exp(x) + exp(2*x) + exp(3*x) + ... + exp(n*x) - n).
%F 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
%t Table[n! SeriesCoefficient[Exp[Exp[x] (Exp[n x] - 1)/(Exp[x] - 1) - n], {x, 0, n}], {n, 0, 15}]
%o (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
%Y Cf. A103438, A319508.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 09 2018