OFFSET
1,5
COMMENTS
This is also the inverted graded generating function for the number of partitions in which no square parts are present
LINKS
Noureddine Chair, Partition Identities From Partial Supersymmetry, arXiv:hep-th/0409011v1, 2004.
James A. Sellers, Partitions Excluding Specific Polygonal Numbers As Parts, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.4.
FORMULA
G.f.: Product_{k>=0}(1+x^k)/(1-(-1)^k*x^(k^2)).
EXAMPLE
a(10)=8 because 10 =8+2 =7+3 =6+4 =5+3+2 =6+2+2 =4+2+2+2 =2+2+2+2+2.
MAPLE
series(product((1+x^k)/(1-(-1)^k*x^(k^2)), k=1..100), x=0, 100);
MATHEMATICA
terms = 56; Product[(1 + x^k)/(1 - (-1)^k*x^(k^2)), {k, 1, terms}] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Dec 14 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Noureddine Chair, Nov 22 2004
STATUS
approved