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A307059
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Expansion of 1/(2 - Product_{k>=1} (1 - x^k)).
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8
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1, -1, 0, 1, -1, 1, -1, 1, 0, -2, 4, -4, 1, 3, -5, 4, -3, 3, -1, -6, 13, -12, 2, 9, -13, 10, -6, 6, -4, -9, 28, -30, 5, 25, -28, 5, 9, 7, -27, 11, 32, -47, 2, 51, -27, -74, 128, -34, -131, 183, -78, -15, -37, 97, 89, -480, 649, -242, -498, 904, -663, 223, -140, 169, 488, -1818
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OFFSET
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0,10
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COMMENTS
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Alternating row sums of Riordan triangle (1, 1 - Product_{j>=1} (1-x^j) ), See A341418(n, m) without column {1, repeat(0)} for m = 0 and n >= 0. - Wolfdieter Lang, Feb 17 2021
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LINKS
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FORMULA
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a(0) = 1; a(n) = Sum_{k=1..n} A010815(k)*a(n-k).
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MATHEMATICA
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nmax=65; CoefficientList[Series[1/(2 - Product[(1 - x^k), {k, 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^j: j in [1..m+2]])) )); // G. C. Greubel, Sep 08 2023
(SageMath)
from sage.modular.etaproducts import qexp_eta
m=80;
def f(x): return 1/(2 - qexp_eta(QQ[['q']], m+2).subs(q=x) )
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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