A153149 Coefficients of the eighth-order mock theta function S_1(q).

1, 0, 0, 1, 1, -1, -1, 1, 2, 0, -2, 1, 2, -2, -2, 2, 3, -1, -2, 2, 2, -3, -4, 3, 5, -2, -4, 3, 5, -4, -6, 4, 7, -4, -7, 5, 7, -6, -9, 7, 11, -6, -10, 7, 11, -9, -14, 9, 15, -9, -14, 11, 16, -13, -19, 13, 21, -12, -22, 15, 23, -18, -26, 19, 30, -19, -30, 21, 31

Offset

0,9

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+2n) (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+2*n) * 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 A153148, A153155, A153156, A153172, A153174, A153176, A153178.

Sequence in context: A360568 A219791 A029345 * A249072 A174007 A330709

Adjacent sequences: A153146 A153147 A153148 * A153150 A153151 A153152

Keyword

sign

Author

Jeremy Lovejoy, Dec 19 2008

Extensions

More terms from Michel Marcus, Feb 23 2015

Status

approved