A153174 Coefficients of the eighth-order mock theta function U_1(q).

0, 1, 0, -1, 1, 2, -1, -2, 1, 3, -1, -4, 2, 5, -2, -6, 3, 8, -4, -9, 4, 11, -5, -14, 7, 17, -7, -20, 9, 24, -11, -28, 12, 33, -15, -39, 18, 46, -20, -53, 24, 62, -28, -72, 32, 83, -37, -96, 43, 110, -48, -126, 56, 145, -65, -165, 72, 188, -83, -214, 95, 243

Offset

0,6

Links

Table of n, a(n) for n=0..61.

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+1)^2)(1+q)(1+q^3)...(1+q^(2n-1))/((1+q^2)(1+q^6)...(1+q^(4n+2))).

Prog

(PARI) lista(nn) = {my(q = qq + O(qq^nn)); gf = sum(n = 0, nn, q^((n+1)^2) * prod(k = 1, n, 1 + q^(2*k-1)) / prod(k = 0, n, 1 + q^(4*k+2))); for (i=0, nn-1, print1(polcoeff(gf, i), ", "); ); } \\ Michel Marcus, Jun 18 2013

Crossrefs

Other '8th-order' mock theta functions are at A153148, A153149, A153155, A153156, A153172, A153176, A153178.

Sequence in context: A322023 A029229 A029216 * A138222 A138224 A181472

Adjacent sequences: A153171 A153172 A153173 * A153175 A153176 A153177

Keyword

sign

Author

Jeremy Lovejoy, Dec 20 2008

Extensions

More terms from Michel Marcus, Feb 23 2015

Status

approved