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A001488
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Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^10 in powers of x.
(Formerly M4703 N2010)
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25
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1, -10, 45, -120, 200, -162, -160, 810, -1530, 1730, -749, -1630, 4755, -7070, 6700, -2450, -5295, 14070, -20010, 19350, -10157, -6290, 25515, -40660, 44940, -34268, 9180, 24510, -57195, 78060, -79087, 56610, -13935, -39600, 89805, -121638, 125405
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OFFSET
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10,2
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = [x^n]( QPochhammer(-x) - 1 )^10. - G. C. Greubel, Sep 04 2023
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MAPLE
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g:= proc(n) option remember; `if`(n=0, 1, add(add([-d, d, -2*d, d]
[1+irem(d, 4)], d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, k) option remember; `if`(k=0, 1, `if`(k=1, `if`(n=0, 0, g(n)),
(q-> add(b(j, q)*b(n-j, k-q), j=0..n))(iquo(k, 2))))
end:
a:= n-> b(n, 10):
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MATHEMATICA
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nmax=46; CoefficientList[Series[(Product[(1-(-x)^j), {j, nmax}] -1)^10, {x, 0, nmax}], x]//Drop[#, 10] & (* Ilya Gutkovskiy, Feb 07 2021 *)
Drop[CoefficientList[Series[(QPochhammer[-x] -1)^10, {x, 0, 102}], x], 10] (* G. C. Greubel, Sep 04 2023 *)
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PROG
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(Magma)
m:=102;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^10 )); // G. C. Greubel, Sep 04 2023
(SageMath)
from sage.modular.etaproducts import qexp_eta
m=100; k=10;
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(N=55, x='x+O('x^N)); Vec((eta(-x)-1)^10) \\ Joerg Arndt, Sep 05 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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