A280947 Expansion of Product_{k>=1} (1 - x^(18*k)) * (1 - x^(18*k-9)) * (1 + x^k) / (1 - x^k).

1, 2, 4, 8, 14, 24, 40, 64, 100, 153, 230, 340, 496, 714, 1016, 1432, 1998, 2764, 3793, 5166, 6988, 9392, 12546, 16664, 22016, 28940, 37860, 49306, 63936, 82568, 106216, 136128, 173844, 221256, 280680, 354952, 447530, 562624, 705352, 881920, 1099840, 1368188

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Andrew Sills, Towards an Automation of the Circle Method, Gems in Experimental Mathematics in Contemporary Mathematics, 2010, formula S78.

Formula

a(n) ~ sqrt(5) * exp(5*Pi*sqrt(n/3)/3) / (4 * 3^(7/4) * n^(3/4)).

Mathematica

nmax=50; CoefficientList[Series[Product[(1-x^(18*k))*(1-x^(18*k-9))*(1+x^k)/(1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Sequence in context: A069251 A261988 A128770 * A069252 A365667 A069253

Adjacent sequences: A280944 A280945 A280946 * A280948 A280949 A280950

Keyword

nonn

Author

Vaclav Kotesovec, Jan 11 2017

Status

approved