%I #9 Feb 07 2020 04:17:24
%S 1,1,2,15,104,1145,13824,208831,3536000,68918769,1489702400,
%T 35742514511,937323767808,26750313223465,824073079660544,
%U 27276657371589375,965004380380626944,36347144974616190689,1451974448007830568960,61319892272079181137679,2729671240750270054400000
%N a(n) = n! * [x^n] 1 / (1 - LambertW(x))^n.
%H Vaclav Kotesovec, <a href="/A332048/b332048.txt">Table of n, a(n) for n = 0..394</a>
%F a(n) = Sum_{k=0..n} Sum_{j=0..n-1} (-1)^(n - k) * binomial(n - 1, j) * Stirling1(j + 1, k) * n^(n + k - j - 1) for n > 0.
%F a(n) ~ phi^(3*n + 1/2) * n^n / (5^(1/4) * exp(n + n/phi)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Feb 07 2020
%t Table[n! SeriesCoefficient[1/(1 - LambertW[x])^n, {x, 0, n}], {n, 0, 20}]
%t Join[{1}, Table[Sum[Sum[(-1)^(n - k) Binomial[n - 1, j] StirlingS1[j + 1, k] n^(n + k - j - 1), {j, 0, n - 1}], {k, 0, n}], {n, 1, 20}]]
%Y Cf. A239761, A277458, A277510.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Feb 06 2020