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%I #6 Oct 04 2017 18:40:04
%S 1,1,12,270,8960,393750,21555072,1413199788,107961384960,
%T 9418192087590,923780000000000,100633991211229476,
%U 12055263261877075968,1575041416811693275900,222887966509090352332800,33962507149515380859375000,5543988061027763016035205120
%N a(n) = n^n*binomial(2*n-1, n).
%C The n-th term of the n-fold convolution of the powers of n.
%F a(n) = [x^n] 1/(1 - n*x)^n.
%F a(n) ~ 2^(2*n-1)*n^n/sqrt(Pi*n).
%t Join[{1}, Table[n^n Binomial[2 n - 1, n], {n, 1, 16}]]
%t Join[{1}, Table[(-1)^n n^n Binomial[-n, n], {n, 1, 16}]]
%t Table[SeriesCoefficient[1/(1 - n x)^n, {x, 0, n}], {n, 0, 16}]
%o (PARI) a(n) = n^n*binomial(2*n-1, n); \\ _Altug Alkan_, Oct 04 2017
%Y Cf. A000312, A001700, A088218.
%Y Cf. A001787, A027472, A036071, A036084, A036226, A038846, A053107, A053108, A053109.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Oct 04 2017
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