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%I #6 Apr 17 2020 07:19:53
%S 1,2,6,35,352,5307,111592,3117900,111259904,4912490375,261954304224,
%T 16560019685937,1222893826048000,104189533522270666,
%U 10132262911996769408,1114216450970154278543,137427598621356912082944,18877351974681584403701519,2869969478954093766868948480
%N a(0) = 1; thereafter a(n) = exp(-1/n) * Sum_{k>=0} (n*k + 1)^n / (n^k * k!).
%H Moussa Benoumhani, <a href="https://doi.org/10.1016/0012-365X(95)00095-E">On Whitney numbers of Dowling lattices</a>, Discrete Math. 159 (1996), no. 1-3, 13-33.
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=0} (x/(1 - x))^k / Product_{j=1..k} (1 - n*j*x/(1 - x)).
%F a(n) = n! * [x^n] exp(x + (exp(n*x) - 1) / n), for n > 0.
%F a(n) = A334165(n,n).
%t Table[SeriesCoefficient[1/(1 - x) Sum[(x/(1 - x))^k/Product[(1 - n j x/(1 - x)), {j, 1, k}], {k, 0, n}], {x, 0, n}], {n, 0, 18}]
%t Join[{1}, Table[n! SeriesCoefficient[Exp[x + (Exp[n x] - 1)/n], {x, 0, n}], {n, 1, 18}]]
%Y Cf. A000110, A007405, A003575, A003576, A003577, A003578, A003579, A003580, A003581, A003582, A301419, A334165.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 16 2020
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