A304625 a(n) = [x^n] Product_{k>=1} ((1 - x^(n*k))/(1 - x^k))^n.

1, 0, 3, 19, 101, 501, 2486, 12398, 62329, 315436, 1605330, 8207552, 42124368, 216903051, 1119974861, 5796944342, 30068145889, 156250892593, 813310723907, 4239676354631, 22130265931880, 115654632452514, 605081974091853, 3168828466966365, 16610409114771876, 87141919856550506

Offset

0,3

Comments

Number of partitions of n into 2 or more parts of n kinds. - Ilya Gutkovskiy, May 16 2018

Links

Table of n, a(n) for n=0..25.

Index entries for sequences related to partitions

Formula

a(n) ~ c * d^n / sqrt(n), where d = A270915 = 5.3527013334866426877724... and c = 0.268015212710733315686... - Vaclav Kotesovec, May 16 2018

Mathematica

Table[SeriesCoefficient[Product[((1 - x^(n k))/(1 - x^k))^n, {k, 1, n}], {x, 0, n}], {n, 0, 25}]
Table[SeriesCoefficient[Product[1/(1 - x^k)^n, {k, 1, n - 1}], {x, 0, n}], {n, 0, 25}]

Crossrefs

Cf. A000065, A008485, A022567, A093160, A270913, A285927, A285928, A286653, A296044, A296162, A296163, A304626.

Sequence in context: A198763 A047029 A095120 * A151539 A305555 A323919

Adjacent sequences: A304622 A304623 A304624 * A304626 A304627 A304628

Keyword

nonn

Author

Ilya Gutkovskiy, May 15 2018

Status

approved