A321042 a(n) = [x^n] Product_{k>=1} (1 + x^k)^sigma_n(k).

1, 1, 5, 37, 491, 12763, 690756, 70250881, 13805853214, 5567873958982, 4386114219458332, 6711687353310594027, 21048327399504558833175, 131214860796100022696745520, 1603892616451767287785208156624, 40296605442098101265893075903063822, 2031406440758379976992019043333960734724

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..80

Formula

a(n) = [x^n] Product_{i>=1, j>=1} (1 + x^(i*j))^(j^n).

a(n) = [x^n] exp(Sum_{k>=1} sigma_(n+1)(k)*x^k/(k*(1 - x^(2*k)))).

Mathematica

Table[SeriesCoefficient[Product[(1 + x^k)^DivisorSigma[n, k], {k, 1, n}], {x, 0, n}], {n, 0, 16}]
Table[SeriesCoefficient[Product[Product[(1 + x^(i j))^(j^n), {j, 1, n}], {i, 1, n}], {x, 0, n}], {n, 0, 16}]
Table[SeriesCoefficient[Exp[Sum[DivisorSigma[n + 1, k] x^k/(k (1 - x^(2 k))), {k, 1, n}]], {x, 0, n}], {n, 0, 16}]

Crossrefs

Cf. A107742, A192065, A288414, A288415, A301548, A301549, A301550, A301551, A301552, A301553, A319647.

Sequence in context: A003709 A361281 A286928 * A244820 A359796 A360933

Adjacent sequences: A321039 A321040 A321041 * A321043 A321044 A321045

Keyword

nonn

Author

Ilya Gutkovskiy, Oct 26 2018

Status

approved