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

%I

%S 1,1,1,1,2,3,4,5,7,9,12,15,19,24,30,37,47,58,72,87,107,130,158,190,

%T 229,275,330,393,469,557,661,780,921,1084,1275,1494,1750,2044,2386,

%U 2777,3231,3750,4348,5030,5815,6711,7738,8905,10240,11757,13488,15449,17680

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

%H Vaclav Kotesovec, <a href="/A280909/b280909.txt">Table of n, a(n) for n = 0..2000</a>

%H Andrew Sills, <a href="https://works.bepress.com/andrew_sills/40/">Rademacher-Type Formulas for Restricted Partition and Overpartition Functions</a>, Ramanujan Journal, 23 (1-3): 253-264, 2010.

%F 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)).

%t 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]

%K nonn

%O 0,5

%A _Vaclav Kotesovec_, Jan 10 2017

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Last modified August 17 03:44 EDT 2022. Contains 356181 sequences. (Running on oeis4.)