A291193 Expansion of 1 + x*(1-x)/(1 + x^2*(1-x^2)/(1 + x^3*(1-x^3)/(1 + x^4*(1-x^4)/(1 + x^5*(1-x^5)/(1 + ...))))), a continued fraction.

1, 1, -1, -1, 1, 2, -1, -4, 0, 6, 3, -7, -8, 6, 15, -2, -24, -9, 33, 32, -35, -68, 20, 114, 25, -164, -120, 196, 285, -160, -521, -16, 796, 423, -1021, -1166, 999, 2310, -387, -3774, -1296, 5194, 4608, -5735, -10007, 3870, 17441, 2750, -25635, -17116, 31111

Offset

0,6

Links

Table of n, a(n) for n=0..50.

Eric Weisstein's World of Mathematics, Mock Theta Function

Formula

G.f.: 1/nu(q) where nu(q) is the '3rd order' mock theta function defined by Sum_{n >= 0} q^(n(n+1))/((1+q)(1+q^3)...(1+q^(2n+1))).

a(n) = (-1)^n*A291200(n). - R. J. Mathar, May 16 2024

Example

G.f. = 1 + x - x^2 - x^3 + x^4 + 2*x^5 - x^6 - 4*x^7 + 6*x^9 + ...

Crossrefs

Cf. A053254 (nu(q)), A291200.

Sequence in context: A126707 A326305 A057458 * A291200 A326143 A011017

Adjacent sequences: A291190 A291191 A291192 * A291194 A291195 A291196

Keyword

sign

Author

Seiichi Manyama, Aug 20 2017

Status

approved