OFFSET
13,2
LINKS
Robert Israel, Table of n, a(n) for n = 13..10000
H. Gupta, On the coefficients of the powers of Dedekind's modular form, J. London Math. Soc., 39 (1964), 433-440.
H. Gupta, On the coefficients of the powers of Dedekind's modular form (annotated and scanned copy)
FORMULA
a(n) = [x^n]( QPochhammer(-x) - 1 )^13. - G. C. Greubel, Sep 07 2023
MAPLE
N:= 100: # to get a(13)..a(N)
G:= (mul(1-(-x)^j, j=1..N)-1)^13:
S:= series(G, x, N+1):
seq(coeff(S, x, n), n=13..N); # Robert Israel, Aug 08 2018
MATHEMATICA
With[{k=13}, Drop[CoefficientList[Series[(QPochhammer[-x] -1)^k, {x, 0, 75}], x], k]] (* G. C. Greubel, Sep 07 2023 *)
PROG
(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
def A047638_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(k, x) ).list()
a=A047638_list(m); a[k:] # G. C. Greubel, Sep 07 2023
(PARI) my(x='x+O('x^40)); Vec((eta(-x)-1)^13) \\ Joerg Arndt, Sep 07 2023
CROSSREFS
KEYWORD
sign
AUTHOR
EXTENSIONS
Definition corrected by Robert Israel, Aug 08 2018
STATUS
approved