A153252 Coefficients of the sixth-order mock theta function psi_{-}(q).

0, 1, 2, 4, 7, 12, 19, 29, 44, 65, 94, 134, 188, 261, 358, 486, 654, 872, 1155, 1519, 1984, 2576, 3325, 4270, 5456, 6939, 8786, 11077, 13912, 17406, 21700, 26961, 33388, 41221, 50739, 62278, 76232, 93067, 113336, 137684, 166873

Offset: 0

Author

Jeremy Lovejoy, Dec 21 2008

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
• B. C. Berndt and S. H. Chan, Sixth order mock theta functions, Adv. Math. 216 (2007), 771-786.

Crossrefs

Cf. A153251.

Other '6th-order' mock theta functions are at A053268, A053269, A053270, A053271, A053272, A053273, A053274.

Programs

PARI

lista(nn) =  q = qq + O(qq^nn); gf = sum(n = 1, nn, q^n * prod(k = 1, 2*n-2, 1 + q^k) / prod(k = 1, n, 1 - q^(2*k-1))); concat(0, Vec(gf)) \\Michel Marcus, Jun 18 2013

Formula

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

a(n) ~ exp(Pi*sqrt(2*n/3)) / (2^(5/2)*sqrt(3*n)). - Vaclav Kotesovec, Jun 13 2019