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A307060
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Expansion of 1/(2 - Product_{k>=1} 1/(1 + x^k)).
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6
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1, -1, 1, -2, 4, -7, 12, -21, 38, -68, 120, -212, 377, -670, 1188, -2107, 3740, -6638, 11778, -20898, 37084, -65808, 116775, -207212, 367696, -652478, 1157815, -2054524, 3645730, -6469316, 11479734, -20370656, 36147506, -64143372, 113821732, -201975429, 358403220, -635982680, 1128544452, -2002589998
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/(2 - Product_{k>=1} (1 - x^(2*k-1))).
a(0) = 1; a(n) = Sum_{k=1..n} A081362(k)*a(n-k).
G.f.: 1/(2 - QPochhammer(x)/QPochhammer(x^2)}.
G.f.: 1/(2 - x^(1/24)*eta(x)/eta(x^2)), where eta(x) is the Dedekind eta function. (End)
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MATHEMATICA
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nmax = 39; CoefficientList[Series[1/(2 - Product[1/(1 + x^k), {k, 1, nmax}]), {x, 0, nmax}], x]
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PROG
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(Magma)
m:=80;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( 1/(2 - (&*[1-x^(2*j-1): j in [1..m+2]])) )); // G. C. Greubel, Jan 24 2024
(SageMath)
m=80;
def f(x): return 1/( 2 - product(1-x^(2*j-1) for j in range(1, m+3)) )
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).list()
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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