A303070 a(n) = [x^n] (1/(1 - x))*Product_{k>=1} 1/(1 - x^k)^n.

1, 2, 8, 35, 164, 787, 3857, 19147, 96004, 485009, 2465013, 12589315, 64555985, 332158127, 1714001409, 8866730665, 45968787524, 238778897128, 1242417984179, 6474394344503, 33784931507529, 176515163156311, 923265560495737, 4834081924982522, 25334170138318345, 132883719945537587

Offset: 0

Author

Ilya Gutkovskiy, Apr 18 2018

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..300
• Index entries for sequences related to partitions

Crossrefs

Main diagonal of A210764.

Cf. A000070, A000713, A008485, A144064, A210843.

Programs

Mathematica

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

Formula

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

a(n) = A210764(n,n) = Sum_{j=0..n} A144064(j,n).

a(n) ~ c * d^n / sqrt(n), where d = A270915 = 5.352701333486642687772415814165... and c = 0.4068869940800214657298372785820... - Vaclav Kotesovec, May 19 2018