A280860 Expansion of Product_{k>=1} ((1-x^(3*k)) * (1-x^(12*k)) / ((1-x^(6*k-5)) * (1-x^(6*k-1)) * (1-x^(4*k)))).

1, 1, 1, 0, 1, 2, 1, 1, 2, 3, 2, 1, 3, 4, 2, 3, 5, 6, 4, 3, 7, 9, 6, 6, 9, 12, 9, 7, 13, 16, 12, 11, 18, 22, 17, 15, 23, 29, 22, 21, 32, 38, 31, 27, 41, 49, 39, 37, 54, 63, 52, 48, 68, 80, 66, 64, 88, 102, 86, 80, 111, 128, 108, 104, 140, 161, 138, 131, 174

Offset

0,6

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Andrew Sills, Rademacher-Type Formulas for Restricted Partition and Overpartition Functions, Ramanujan Journal, 23 (1-3): 253-264, 2010 [equation (2.6)].

Formula

a(n) ~ exp(sqrt(n)*Pi/3) / (3*sqrt(2*n)).

Mathematica

nmax = 100; CoefficientList[Series[Product[(1-x^(3*k)) * (1-x^(12*k)) / ((1-x^(6*k-5)) * (1-x^(6*k-1)) * (1-x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Sequence in context: A329750 A030496 A005794 * A208993 A328029 A201384

Adjacent sequences: A280857 A280858 A280859 * A280861 A280862 A280863

Keyword

nonn

Author

Vaclav Kotesovec, Jan 09 2017

Status

approved