A291200 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

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Mock Theta Function

Formula

a(n) = (-1)^n * A291193(n).

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))).

G.f.: 1/Sum_{n >= 0} q^(n(n+1))/((1-q)*(1-q^3)...(1-q^(2n+1)).

Crossrefs

Cf. A067357, A291193.

Sequence in context: A326305 A057458 A291193 * A326143 A011017 A348508

Adjacent sequences: A291197 A291198 A291199 * A291201 A291202 A291203

Keyword

sign

Author

Seiichi Manyama, Aug 20 2017

Status

approved