A302239 Expansion of Product_{k>=1} ((1 + x^k)/(1 - x^k))^p(k), where p(k) = number of partitions of k (A000041).

1, 2, 6, 16, 40, 96, 226, 512, 1140, 2488, 5336, 11270, 23494, 48356, 98438, 198338, 395846, 783136, 1536800, 2992818, 5786952, 11114950, 21213906, 40247696, 75928804, 142475644, 265985628, 494155176, 913802164, 1682338192, 3084101744, 5630853218, 10240484332, 18553818210

Offset

0,2

Comments

Convolution of the sequences A001970 and A261049.

Links

Table of n, a(n) for n=0..33.

N. J. A. Sloane, Transforms

Formula

G.f.: Product_{k>=1} ((1 + x^k)/(1 - x^k))^A000041(k).

Mathematica

nmax = 33; CoefficientList[Series[Product[((1 + x^k)/(1 - x^k))^PartitionsP[k], {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000041, A001970, A015128, A156616, A206622, A206623, A206624, A260916, A261049, A261386, A261452, A261519, A261520, A301554, A301555, A302237, A302238.

Sequence in context: A265725 A129952 A057711 * A264551 A293004 A265278

Adjacent sequences: A302236 A302237 A302238 * A302240 A302241 A302242

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 03 2018

Status

approved