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%I #10 Dec 04 2018 20:40:19
%S 0,1,3,5,-650,-46071,3121776,5538166381,3146076001776,
%T -10459815889305231,-100694615309371571840,-193538025548431984737219,
%U 38912028315765820944424730112,2554132880645627969533690819801657,-106074951996903194289368162206783509504
%N a(n) = n! * [x^n] log(1 + Sum_{k>=1} k^n*x^k/k!).
%C a(n) is the n-th term of the logarithmic transform of the n-th powers.
%H Alois P. Heinz, <a href="/A320939/b320939.txt">Table of n, a(n) for n = 0..77</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%p seq(coeff(series(factorial(n)*log(1+add(k^n*x^k/factorial(k),k=1..n)),x,n+1), x, n), n = 0 .. 15); # _Muniru A Asiru_, Oct 28 2018
%t Table[n! SeriesCoefficient[Log[1 + Sum[k^n x^k/k!, {k, 1, n}]], {x, 0, n}], {n, 0, 14}]
%Y Cf. A009306, A033464, A279644, A300452.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Oct 28 2018