OFFSET
0,3
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Michael Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
FORMULA
EXAMPLE
1 + x + 3*x^2 + 6*x^3 + 11*x^4 + 20*x^5 + 34*x^6 + 56*x^7 + 91*x^8 + ...
MATHEMATICA
f[x_, y_] := QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; A185083[n_] := SeriesCoefficient[(1/2)*(f[x^2, x^2]/f[-x, -x] + 1), {x, 0, n}]; Table[A185083[n], {n, 0, 50}] (* G. C. Greubel, Jun 22 2017 *)
PROG
(PARI) {a(n) = local(A); if( n<0, 0, n = 2*n; A = x * O(x^n); polcoeff( (eta(x^2 + A)^3 / (eta(x + A)^2 * eta(x^4 + A)) + 1) / 2, n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Mar 02 2012
STATUS
approved