OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Partition Function b_k
FORMULA
G.f.: 1/(1 - x*Product_{k>=1} (1 - x^(4*k))/(1 - x^k)).
G.f.: 1/(1 - x*Product_{k>=1} (1 + x^k + x^(2*k) + x^(3*k))).
a(0) = 1; a(n) = Sum_{k=1..n} A001935(k-1)*a(n-k).
MATHEMATICA
nmax = 33; CoefficientList[Series[1/(1 - x Product[(1 + x^(2 k))/(1 - x^(2 k - 1)), {k, 1, nmax}]), {x, 0, nmax}], x]
nmax = 33; CoefficientList[Series[1/(1 + (1 - x) QPochhammer[-1, x^2]/(2 QPochhammer[1/x, x^2])), {x, 0, nmax}], x]
nmax = 33; CoefficientList[Series[1/(1 - x EllipticTheta[2, 0, x]/(Sqrt[2] x^(1/8) EllipticTheta[2, Pi/4, Sqrt[x]])), {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 30 2018
STATUS
approved