This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A032803 #14 Jul 08 2025 19:42:19
%S A032803 1,1,3,5,11,23,47,99,203,423,877,1819,3777,7831,16253,33715,69953,
%T A032803 145137,301113,624745,1296165,2689221,5579425,11575849,24016893,
%U A032803 49828757,103381739,214490133,445011179,923282285,1915570171,3974309213,8245656195,17107588781
%N A032803 Expansion of Sum_{i>=0} q^i*theta_3^i.
%F A032803 From _Vaclav Kotesovec_, Jun 26 2020: (Start)
%F A032803 G.f.: 1/(1 - x*EllipticTheta(3,x)).
%F A032803 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 A032803 (End)
%t A032803 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 A032803 nonn
%O A032803 0,3
%A A032803 _N. J. A. Sloane_
%E A032803 More terms from _Sean A. Irvine_, Jun 26 2020