A153172 Coefficients of the eighth-order mock theta function U_0(q).

1, 1, 1, 0, 1, 0, -1, 1, 0, 1, 2, -1, 0, -1, -1, 1, 0, 2, 1, 0, 1, -2, -2, 1, 0, 2, 3, -2, 0, -2, -2, 2, -1, 3, 3, -1, 1, -2, -4, 2, 0, 2, 4, -3, 1, -4, -4, 3, -1, 5, 5, -2, 2, -4, -6, 3, -2, 5, 7, -4, 0, -6, -6, 4, -1, 7, 7, -4, 3, -7, -9, 5, -1, 7, 10, -6, 1

Offset

0,11

Links

Table of n, a(n) for n=0..76.

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

Formula

U_0(q) = Sum_{n >= 0} q^(n^2) (1+q)(1+q^3)...(1+q^(2n-1))/((1+q^4)(1+q^8)...(1+q^(4n))).

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^(4*k))); Vec(gf) \\ Michel Marcus, Jun 18 2013

Crossrefs

Other '8th-order' mock theta functions are at A153148, A153149, A153155, A153156, A153174, A153176, A153178.

Sequence in context: A354512 A088705 A065712 * A242498 A321927 A016194

Adjacent sequences: A153169 A153170 A153171 * A153173 A153174 A153175

Keyword

sign

Author

Jeremy Lovejoy, Dec 20 2008

Extensions

More terms from Michel Marcus, Feb 23 2015

Status

approved