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%I #13 Oct 09 2018 07:58:08
%S 1,1,5,44,723,24655,1715816,239697569,69557364821,41297123651644,
%T 49900451628509015,125141540794392423599,641579398300246011553552,
%U 6729809577032172543373047313,146355880526667013027682326650073,6505380999057202235872595196799580684
%N a(n) = [x^n] 1/(1 - Sum_{k>=1} k^n*x^k).
%C Number of compositions (ordered partitions) of n where there are k^n sorts of part k.
%C a(n) is the n-th term of invert transform of n-th powers.
%H Vaclav Kotesovec, <a href="/A301655/b301655.txt">Table of n, a(n) for n = 0..79</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F a(n) = [x^n] 1/(1 - PolyLog(-n,x)), where PolyLog() is the polylogarithm function.
%F From _Vaclav Kotesovec_, Mar 27 2018: (Start)
%F a(n) ~ 3^(n^2/3) if mod(n,3)=0
%F a(n) ~ 3^(n*(n-4)/3-2)*2^(2*n-1)*(n-1)*(n+8) if mod(n,3)=1
%F a(n) ~ 3^((n+1)*(n-3)/3)*2^n*(n+1) if mod(n,3)=2
%F (End)
%t Table[SeriesCoefficient[1/(1 - Sum[k^n x^k, {k, 1, n}]), {x, 0, n}], {n, 0, 15}]
%t Table[SeriesCoefficient[1/(1 - PolyLog[-n, x]), {x, 0, n}], {n, 0, 15}]
%Y Main diagonal of A320251.
%Y Cf. A001906, A033453, A053506, A144109, A193678, A221460, A252782, A292194.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Mar 25 2018