A153251 Coefficients of the sixth-order mock theta function phi_{-}(q).

0, 1, 3, 5, 8, 14, 22, 33, 51, 74, 105, 151, 210, 289, 398, 537, 719, 960, 1267, 1660, 2167, 2807, 3614, 4638, 5915, 7507, 9498, 11957, 14994, 18744, 23337, 28959, 35834, 44192, 54338, 66643, 81499, 99407, 120969, 146836, 177820

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. A153252.

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-1, 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-1))/((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