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A317910
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Expansion of -1/(1 - x)^2 + (1/(1 - x))*Product_{k>=1} (1 + x^k).
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2
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0, 0, 0, 1, 2, 4, 7, 11, 16, 23, 32, 43, 57, 74, 95, 121, 152, 189, 234, 287, 350, 425, 513, 616, 737, 878, 1042, 1233, 1454, 1709, 2004, 2343, 2732, 3179, 3690, 4274, 4941, 5700, 6563, 7544, 8656, 9915, 11340, 12949, 14764, 16811, 19114, 21703, 24612, 27875, 31532, 35628, 40209
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OFFSET
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0,5
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COMMENTS
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LINKS
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FORMULA
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G.f.: -1/(1 - x)^2 + (1/(1 - x))*Product_{k>=1} 1/(1 - x^(2*k-1)).
a(n) ~ 3^(1/4) * exp(Pi*sqrt(n/3)) / (2*Pi*n^(1/4)). - Vaclav Kotesovec, Aug 21 2018
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MAPLE
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a:=series(-1/(1-x)^2+(1/(1-x))*mul((1 + x^k), k=1..100), x=0, 53): seq(coeff(a, x, n), n=0..52); # Paolo P. Lava, Apr 02 2019
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MATHEMATICA
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nmax = 52; CoefficientList[Series[-1/(1 - x)^2 + 1/(1 - x) Product[1 + x^k, {k, 1, nmax}], {x, 0, nmax}], x] (* or *)
nmax = 52; CoefficientList[Series[1/((1 - x) QPochhammer[x, x^2]) - 1/(1 - x)^2, {x, 0, nmax}], x] (* or *)
Table[Sum[PartitionsQ[k] - 1, {k, 0, n}] , {n, 0, 52}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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