OFFSET
0,2
FORMULA
G.f.: (1 + x)/theta_4(x), where theta_4() is the Jacobi theta function.
a(n) ~ exp(Pi*sqrt(n)) / (4*n) * (1 - (Pi/4 + 1/Pi)/sqrt(n)). - Vaclav Kotesovec, Jul 20 2019
MATHEMATICA
nmax = 42; CoefficientList[Series[(1 + x) Product[(1 + x^k)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]
a[n_] := a[n] = Sum[PartitionsP[k] PartitionsQ[n - k], {k, 0, n}]; Table[a[n] + a[n - 1], {n, 0, 42}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 20 2019
STATUS
approved