A320255 a(n) = n! * [x^n] log(1 + exp(x)*(x + (n/2 - 1)*x^2)).

0, 1, 1, -1, -26, 39, 3666, -7400, -1488416, 3802113, 1322570530, -4095154284, -2187371499312, 7964242253473, 6052757424558586, -25343867475914910, -25988018018090461664, 123032891453320498449, 163684285184147641156098, -864557405968781387651984, -1448111703094244548802632160

Offset: 0

Author

Ilya Gutkovskiy, Oct 08 2018

Keywords

• sign

Comments

For n > 2, a(n) is the n-th term of the logarithmic transform of n-gonal numbers.

Links

• N. J. A. Sloane, Transforms
• Index to sequences related to polygonal numbers

Crossrefs

Cf. A009306, A033464, A300455, A318118, A318124, A320254.

Programs

Mathematica

Table[n! SeriesCoefficient[Log[1 + Exp[x] (x + (n/2 - 1) x^2)], {x, 0, n}], {n, 0, 20}]