A147766 -id:A147766 - cp's OEIS frontend

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

Ilya Gutkovskiy, Sep 25 2018

nonn

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

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

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

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}]

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

A147767 Triangle read by rows, square of A116598.

Original entry on oeis.org

1, 0, 1, 2, 0, 1, 2, 2, 0, 1, 5, 2, 2, 0, 1, 6, 5, 2, 2, 0, 1, 6, 5, 2, 2, 0, 1, 13, 6, 5, 2, 2, 0, 1, 16, 13, 6, 5, 2, 2, 0, 1, 30, 16, 13, 6, 5, 2, 2, 0, 1, 40, 30, 16, 13, 6, 5, 2, 2, 0, 1, 40, 30, 16, 13, 6, 5, 2, 2, 0, 1

Offset: 0

Gary W. Adamson, Nov 11 2008

Row sums = A000990: (1, 1, 3, 5, 10, 16, 29, 45, ...).

			First few rows of the triangle:
   1;
   0,  1;
   2,  0, 1;
   2,  2, 0, 1;
   5,  2, 2, 0, 1;
   6,  5, 2, 2, 0, 1;
  13,  6, 5, 2, 2, 0, 1;
  16, 13, 6, 5, 2, 2, 0, 1;
  ...

Cf. A147766, A000990.

Triangle read by rows, A116598^2. A147766 in every column.

Typo in formula corrected by Olivier Gérard, Jul 25 2016

cp's OEIS Frontend

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

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