%I #5 Oct 08 2018 18:15:40
%S 0,1,1,-1,-26,39,3666,-7400,-1488416,3802113,1322570530,-4095154284,
%T -2187371499312,7964242253473,6052757424558586,-25343867475914910,
%U -25988018018090461664,123032891453320498449,163684285184147641156098,-864557405968781387651984,-1448111703094244548802632160
%N a(n) = n! * [x^n] log(1 + exp(x)*(x + (n/2 - 1)*x^2)).
%C For n > 2, a(n) is the n-th term of the logarithmic transform of n-gonal numbers.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%t Table[n! SeriesCoefficient[Log[1 + Exp[x] (x + (n/2 - 1) x^2)], {x, 0, n}], {n, 0, 20}]
%Y Cf. A009306, A033464, A300455, A318118, A318124, A320254.
%K sign
%O 0,5
%A _Ilya Gutkovskiy_, Oct 08 2018
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