A153148 Coefficients of the eighth-order mock theta function S_0(q).

1, 1, 1, -1, 0, 2, 0, -1, 0, 1, 1, -2, 0, 3, 0, -2, -1, 3, 1, -4, 0, 4, 1, -4, -1, 5, 2, -6, -2, 7, 0, -6, -1, 7, 3, -9, -1, 10, 1, -10, -2, 11, 3, -14, -3, 15, 2, -14, -3, 17, 5, -19, -4, 21, 3, -22, -5, 23, 7, -28, -5, 30, 5, -30, -7, 34, 8, -38, -7, 41, 7

Offset

0,6

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

B. Gordon and R. J. McIntosh, Some eighth order mock theta functions, J. London Math. Soc. 62 (2000), 321-335.

Formula

G.f.: Sum_{n >= 0} q^(n^2)(1+q)(1+q^3)...(1+q^(2n-1))/(1+q^2)(1+q^4)...(1+q^(2n)).

Prog

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

Crossrefs

Other '8th-order' mock theta functions are at A153149, A153155, A153156, A153172, A153174, A153176, A153178.

Sequence in context: A091991 A108234 A324572 * A378437 A091830 A029427

Adjacent sequences: A153145 A153146 A153147 * A153149 A153150 A153151

Keyword

sign

Author

Jeremy Lovejoy, Dec 19 2008

Extensions

More terms from Michel Marcus, Feb 23 2015

Status

approved