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A047638
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Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^13 in powers of x.
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22
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1, -13, 78, -286, 702, -1131, 845, 1300, -5928, 11583, -13715, 5915, 15834, -47477, 73658, -71201, 20436, 79391, -198796, 280345, -258557, 92807, 200850, -536341, 773916, -768222, 432705, 204477, -979628, 1626196, -1856569, 1471184, -452192
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OFFSET
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13,2
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LINKS
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FORMULA
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a(n) = [x^n]( QPochhammer(-x) - 1 )^13. - G. C. Greubel, Sep 07 2023
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MAPLE
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N:= 100: # to get a(13)..a(N)
G:= (mul(1-(-x)^j, j=1..N)-1)^13:
S:= series(G, x, N+1):
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MATHEMATICA
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With[{k=13}, Drop[CoefficientList[Series[(QPochhammer[-x] -1)^k, {x, 0, 75}], x], k]] (* G. C. Greubel, Sep 07 2023 *)
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PROG
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(Magma)
m:=80;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^(13) )); // G. C. Greubel, Sep 07 2023
(SageMath)
from sage.modular.etaproducts import qexp_eta
m=75; k=13;
def f(k, x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(k, x) ).list()
(PARI) my(x='x+O('x^40)); Vec((eta(-x)-1)^13) \\ Joerg Arndt, Sep 07 2023
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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