A032803 Expansion of Sum_{i>=0} q^i*theta_3^i.

1, 1, 3, 5, 11, 23, 47, 99, 203, 423, 877, 1819, 3777, 7831, 16253, 33715, 69953, 145137, 301113, 624745, 1296165, 2689221, 5579425, 11575849, 24016893, 49828757, 103381739, 214490133, 445011179, 923282285, 1915570171, 3974309213, 8245656195, 17107588781

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Programs

Mathematica

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 *)

Formula

From Vaclav Kotesovec, Jun 26 2020: (Start)

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

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...

(End)

Extensions

More terms from Sean A. Irvine, Jun 26 2020