A277349 Expansion of Product_{k>=1} 1/(1 - x^(6*k+1)).
1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 1, 0, 1, 3, 3, 2, 1, 1, 1, 3, 4, 3, 2, 1, 2, 4, 5, 5, 3, 2, 2, 5, 7, 6, 5, 3, 3, 6, 9, 9, 7, 5, 4, 7, 11, 12, 10, 7, 6, 9, 14, 16, 14, 11, 8, 11, 17, 20, 19, 15, 12, 14, 21, 26, 25, 21, 17, 18, 26, 32, 33, 28, 23, 24, 32, 41
Offset: 0
Keywords
Examples
a(26) = 2, because we have [19, 7] and [13, 13].
Links
Programs
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Maple
N:= 100: G:= 1/mul(1-x^m,m=7..N,6): S:= series(G,x,N+1): seq(coeff(S,x,j),j=0..N); # Robert Israel, Jan 23 2019
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Mathematica
CoefficientList[Series[(1 - x)/QPochhammer[x, x^6], {x, 0, 100}], x]
Formula
G.f.: Product_{k>=1} 1/(1 - x^(6*k+1)).
a(n) ~ Pi^(1/6) * Gamma(1/6) * exp(sqrt(n)*Pi/3) / (24*sqrt(3)*n^(13/12)). - Vaclav Kotesovec, Oct 10 2016
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