A319670 a(n) = [x^n] Product_{k>=2} 1/(1 - x^k)^n.

1, 0, 2, 3, 14, 30, 119, 301, 1078, 3036, 10242, 30624, 100451, 310128, 1004817, 3158343, 10182982, 32345186, 104145896, 332953929, 1072383374, 3442913407, 11100120528, 35742258497, 115377720235, 372326184555, 1203406838428, 3890040945078, 12588182588373, 40748118469180

Offset

0,3

Comments

Number of partitions of n into parts > 1, if there are n kinds of parts.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..1000

Formula

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

a(n) ~ c * d^n / sqrt(n), where d = 3.293558598422332665054219310876308... and c = 0.2154241499279313950113565475... - Vaclav Kotesovec, Oct 06 2018

Mathematica

Table[SeriesCoefficient[Product[1/(1 - x^k)^n , {k, 2, n}], {x, 0, n}], {n, 0, 29}]
Table[SeriesCoefficient[((1 - x)/QPochhammer[x])^n, {x, 0, n}], {n, 0, 29}]
Table[SeriesCoefficient[Exp[n Sum[(DivisorSigma[1, k] - 1) x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 29}]

Crossrefs

Cf. A000203, A002865, A008485, A147766, A191659, A304625, A319671.

Sequence in context: A101005 A029998 A117461 * A047005 A338513 A080017

Adjacent sequences: A319667 A319668 A319669 * A319671 A319672 A319673

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 25 2018

Status

approved