OFFSET
2,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..1002
FORMULA
G.f.: (-1 + Product_{k>=1} (1 + x^(2*k - 1)))^2.
a(n) = [x^n]( (2/QPochhammer(-1,-x) - 1)^2 ). - G. C. Greubel, Sep 07 2023
MATHEMATICA
nmax = 55; CoefficientList[Series[(-1 + Product[1/(1 + (-x)^k), {k, 1, nmax}])^2, {x, 0, nmax}], x] // Drop[#, 2] &
With[{k=2}, Drop[CoefficientList[Series[(2/QPochhammer[-1, -x] -1)^k, {x, 0, 80}], x], k]] (* G. C. Greubel, Sep 07 2023 *)
PROG
(Magma)
m:=80;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( (-1 + (&*[1+x^(2*j+1): j in [0..m+2]]) )^2 )); // G. C. Greubel, Sep 07 2023
(SageMath)
m=80
def f(x): return (-1 + product(1+x^(2*j-1) for j in range(1, m+3)) )^2
def A338463_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).list()
a=A338463_list(m); a[2:] # G. C. Greubel, Sep 07 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2021
STATUS
approved