OFFSET
1,2
REFERENCES
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
M. Kontsevich and D. Zagier, Periods, pp. 771-808 of B. Engquist and W. Schmid, editors, Mathematics Unlimited - 2001 and Beyond, 2 vols., Springer-Verlag, 2001.
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
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: (eta(z)*eta(6*z)/(eta(2*z)*eta(3*z)))^12.
a(n) = [x^n]( QPochhammer(-x) - 1 )^12. - G. C. Greubel, Sep 05 2023
MATHEMATICA
With[{k=12}, Drop[CoefficientList[Series[(QPochhammer[-x] -1)^k, {x, 0, 102}], x], k]] (* 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)^(12) )); // G. C. Greubel, Sep 05 2023
(SageMath)
from sage.modular.etaproducts import qexp_eta
m=100; k=12;
def f(k, x): return (-1 + qexp_eta(QQ[['q']], m+2).subs(q=-x) )^k
def A001490_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(k, x) ).list()
a=A001490_list(m); a[k:] # G. C. Greubel, Sep 05 2023
(PARI) my(N=55, x='x+O('x^N)); Vec((eta(-x)-1)^12) \\ Joerg Arndt, Sep 05 2023
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved
