A304626 a(n) = [x^n] Product_{k>=1} ((1 + x^k)/(1 + x^(n*k)))^n.

1, 0, 1, 10, 47, 201, 849, 3578, 15147, 64516, 276268, 1188342, 5130987, 22226036, 96543989, 420368843, 1834203939, 8018057328, 35107961157, 153950675566, 675978772306, 2971700764920, 13078268135661, 57613905606250, 254038914924767, 1121081799217206, 4951199308679965

Offset: 0

Author

Ilya Gutkovskiy, May 15 2018

Keywords

• nonn

Comments

Number of partitions of n into 2 or more distinct parts, with n types of each part. - Ilya Gutkovskiy, May 16 2018

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A058576, A073252, A111133, A255526, A270913, A304625.

Programs

Mathematica

Table[SeriesCoefficient[Product[((1 + x^k)/(1 + x^(n k)))^n, {k, 1, n}], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[Product[(1 + x^k)^n, {k, 1, n - 1}], {x, 0, n}], {n, 0, 26}]
Table[SeriesCoefficient[(QPochhammer[-1, x, 1 + n]/QPochhammer[-1, x^n, 1 + n])^n, {x, 0, n}], {n, 0, 26}]

Formula

a(n) ~ c * d^n / sqrt(n), where d = A270914 = 4.502476747617354487738... and c = 0.2605422331424384694... - Vaclav Kotesovec, May 16 2018