A304782 a(n) = [x^n] (1/(1 - x))*Product_{k>=1} (1 + n*x^k).

1, 2, 5, 19, 49, 126, 469, 1177, 2881, 6481, 23101, 53725, 127153, 274288, 581925, 1860751, 4155649, 9279791, 19409221, 39839239, 77052401, 229393207, 481747949, 1035561408, 2082441025, 4153434376, 7822058869, 14686515649, 39394280689, 79657493191, 163600884901

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Index entries for sequences related to partitions

Formula

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

a(n) = Sum_{j=0..n} A286957(j,n).

Mathematica

Table[SeriesCoefficient[1/(1 - x) Product[(1 + n x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/(1 - x) Exp[Sum[(-1)^(k + 1) n^k x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[QPochhammer[-n, x]/((1 + n) (1 - x)), {x, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A286957, A291698, A303070, A303071, A303914.

Sequence in context: A077323 A215274 A293457 * A184435 A112266 A287019

Adjacent sequences: A304779 A304780 A304781 * A304783 A304784 A304785

Keyword

nonn

Author

Ilya Gutkovskiy, May 18 2018

Status

approved