OFFSET
0,2
COMMENTS
Partial sums of A000726.
LINKS
Eric Weisstein's World of Mathematics, Partition Function b_k
FORMULA
G.f.: (1/(1 - x))*Product_{k>=0} 1/((1 - x^(3*k+1))*(1 - x^(3*k+2))).
G.f.: (1/(1 - x))*Product_{k>=1} (1 + x^k + x^(2*k)).
a(n) ~ exp(2*Pi*sqrt(n)/3) / (2*Pi*n^(1/4)). - Vaclav Kotesovec, May 18 2018
MATHEMATICA
nmax = 50; CoefficientList[Series[1/(1 - x) Product[(1 - x^(3 k))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[1/(1 - x) Product[1/((1 - x^(3 k + 1)) (1 - x^(3 k + 2))), {k, 0, nmax}], {x, 0, nmax}], x]
nmax = 50; CoefficientList[Series[1/(1 - x) Product[(1 + x^k + x^(2 k)), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 15 2018
STATUS
approved