A321261 a(n) = [x^n] Product_{k>=1} (1 + x^k)^(sigma_n(k)-k^n).

1, 0, 1, 1, 17, 2, 859, 131, 105508, 40907, 72916903, 6834168, 228239366293, 27616985835, 2050004858009336, 352807044193881, 87173272463714343166, 6798224808203572198, 18318379579349549499397403, 1187836799227050499295342, 11258903016282277676462826232428

Offset: 0

Author

Ilya Gutkovskiy, Nov 01 2018

Keywords

• nonn

Crossrefs

Cf. A281268, A318844, A319107, A321042, A321258, A321260.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1 + x^k)^(DivisorSigma[n, k] - k^n), {k, 1, n}], {x, 0, n}], {n, 0, 20}]
Table[SeriesCoefficient[Exp[Sum[Sum[(-1)^(k/d + 1) d (DivisorSigma[n, d] - d^n), {d, Divisors[k]}] x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 20}]

Formula

a(n) = [x^n] exp(Sum_{k>=1} ( Sum_{d|k} (-1)^(k/d+1)*d*(sigma_n(d) - d^n) ) * x^k/k).