OFFSET
0,8
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011, 2004.
FORMULA
G.f.: Product_{k>0} (1+x^(2*k-1))/(1-(-1)^k*x^(k^2)).
EXAMPLE
a(16)=6 because 16 = 13+3 = 11+5 = 7+5+4 = 5+3+4+4 = 4+4+4+4.
MAPLE
series(product((1+x^(2*k-))/(1-(-1)^k*x^(k^2)), k=1..100), x=0, 100);
MATHEMATICA
With[{m=80}, CoefficientList[Series[Product[(1+x^(2*k-1))/(1-(-1)^k *x^(k^2)), {k, m+2}], {x, 0, m}], x]] (* G. C. Greubel, Mar 28 2023 *)
PROG
(Magma)
m:=80;
f:= func< x | (&*[(1+x^(2*k-1))/(1-(-1)^k*x^(k^2)): k in [1..m+2]]) >;
R<x>:=PowerSeriesRing(Integers(), m);
Coefficients(R!( f(x) )); // G. C. Greubel, Mar 28 2023
(SageMath)
m=80
def f(x): return product( (1+x^(2*k-1))/(1-(-1)^k*x^(k^2)) for k in range(1, m+2))
def A100522_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( f(x) ).list()
A100522_list(m) # G. C. Greubel, Mar 28 2023
CROSSREFS
Cf. A100926.
KEYWORD
nonn
AUTHOR
Noureddine Chair, Nov 25 2004
EXTENSIONS
Offset corrected by G. C. Greubel, Mar 28 2023
STATUS
approved