OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{k=0..n} A015128(k).
a(n) ~ exp(Pi*sqrt(n))/(4*Pi*sqrt(n)) * (1 + Pi/(4*sqrt(n))).
G.f.: 1/(1-x) * Product_{k>=1} (1 + x^k) / (1 - x^k). - Vaclav Kotesovec, Mar 25 2017
G.f.: 1/((1 - x)*theta_4(x)), where theta_4() is the Jacobi theta function. - Ilya Gutkovskiy, Apr 20 2018
MATHEMATICA
Accumulate[Table[Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}], {n, 0, 50}]]
nmax = 50; CoefficientList[Series[1/(1-x) * Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 25 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Oct 25 2016
STATUS
approved