

A153174


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


8



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
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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), 321335.


FORMULA

G.f: Sum_{n >= 0} q^((n+1)^2)(1+q)(1+q^3)...(1+q^(2n1))/((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*k1)) / prod(k = 0, n, 1 + q^(4*k+2))); for (i=0, nn1, 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: A224708 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



