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A001484
Expansion of (Product_{j>=1} (1-(-x)^j) - 1)^6 in powers of x.
(Formerly M4107 N1704)
5
1, -6, 15, -20, 9, 24, -65, 90, -75, 6, 90, -180, 220, -180, 66, 110, -264, 360, -365, 264, -66, -178, 375, -510, 496, -414, 180, 60, -330, 570, -622, 582, -390, 220, 96, -300, 621, -630, 705, -492, 300, 0, -235, 420, -570, 594, -735, 420, -420, -120, 219, -586, 360
OFFSET
6,2
REFERENCES
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).
LINKS
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
FORMULA
a(n) = [x^n] ( QPochhammer(-x) - 1 )^6. - G. C. Greubel, Sep 04 2023
MAPLE
N:= 100:
S:= series((mul(1-(-x)^j, j=1..N)-1)^6, x, N+1):
seq(coeff(S, x, j), j=6..N); # Robert Israel, Feb 05 2019
MATHEMATICA
Drop[CoefficientList[Series[(QPochhammer[-x] -1)^6, {x, 0, 102}], x], 6] (* G. C. Greubel, Sep 04 2023 *)
PROG
(Magma)
m:=102;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( ((&*[1-(-x)^j: j in [1..m+2]]) -1)^6 )); // G. C. Greubel, Sep 04 2023
(SageMath)
m=100; k=6;
def f(k, x): return (-1 + product( (1+x^j)*(1-x^(2*j))/(1+x^(2*j)) for j in range(1, m+2) ) )^k
def A001484_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(k, x) ).list()
a=A001484_list(m); a[k:] # G. C. Greubel, Sep 04 2023
(PARI) my(N=70, x='x+O('x^N)); Vec((eta(-x)-1)^6) \\ Joerg Arndt, Sep 04 2023
KEYWORD
sign
EXTENSIONS
Edited by Robert Israel, Feb 05 2019
STATUS
approved