A280909 Expansion of Product_{k>=1} ((1-x^(12*k)) * (1-x^(12*k-10)) * (1-x^(12*k-9)) / (1-x^k)).

1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 12, 15, 19, 24, 30, 37, 47, 58, 72, 87, 107, 130, 158, 190, 229, 275, 330, 393, 469, 557, 661, 780, 921, 1084, 1275, 1494, 1750, 2044, 2386, 2777, 3231, 3750, 4348, 5030, 5815, 6711, 7738, 8905, 10240, 11757, 13488, 15449, 17680

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..2000

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

Formula

a(n) ~ 3^(1/12) * Pi^(19/12) * exp(Pi*sqrt(n/2)) / (Gamma(1/4) * Gamma(1/6) * 2^(35/24) * n^(25/24)).

Mathematica

nmax = 60; CoefficientList[Series[Product[(1-x^(12*k)) * (1-x^(12*k-10)) * (1-x^(12*k-9)) / (1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Sequence in context: A039853 A062188 A122129 * A003413 A100853 A174065

Adjacent sequences: A280906 A280907 A280908 * A280910 A280911 A280912

Keyword

nonn

Author

Vaclav Kotesovec, Jan 10 2017

Status

approved