A032803 - OEIS

%I #12 Jun 26 2020 03:31:29

%S 1,1,3,5,11,23,47,99,203,423,877,1819,3777,7831,16253,33715,69953,

%T 145137,301113,624745,1296165,2689221,5579425,11575849,24016893,

%U 49828757,103381739,214490133,445011179,923282285,1915570171,3974309213,8245656195,17107588781

%N Expansion of Sum_{i>=0} q^i*theta_3^i.

%F From _Vaclav Kotesovec_, Jun 26 2020: (Start)

%F G.f.: 1/(1 - x*EllipticTheta(3,x)).

%F a(n) ~ c / r^n, where r = 0.48198821952392600540358080089338068467918852426... is the root of the equation r*EllipticTheta(3,r) = 1 and c = 1 / (1 + r^2 * EllipticTheta'(3,r)) = 0.59345908175794984247602713305661895068944878811545062...

%F (End)

%t nmax = 50; CoefficientList[Series[Sum[x^k*EllipticTheta[3, x]^k, {k, 0, nmax}], {x, 0, nmax}], x] (* or *) nmax = 50; CoefficientList[Series[1/(1 - x*EllipticTheta[3, x]), {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 26 2020 *)

%K nonn

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Sean A. Irvine_, Jun 26 2020