A153176 Coefficients of the eighth-order mock theta function V_0(q).

1, 2, 4, 4, 6, 8, 8, 12, 16, 18, 24, 28, 32, 40, 48, 56, 66, 80, 92, 108, 128, 144, 168, 196, 224, 258, 296, 336, 384, 440, 496, 564, 640, 720, 816, 920, 1030, 1160, 1304, 1456, 1632, 1824, 2032, 2268, 2528, 2808, 3120, 3468, 3840, 4258, 4716, 5208, 5760, 6360

Offset

0,2

Links

Vaclav Kotesovec, 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

V_0(q) = -1 + 2*Sum_{n >= 0} q^(n^2)(1+q)(1+q^3)...(1+q^(2n-1))/((1-q)(1-q^3)...(1-q^(2n-1))).

a(n) ~ exp(Pi*sqrt(n)/2) / (2*sqrt(n)). - Vaclav Kotesovec, Jun 12 2019

Mathematica

nmax = 100; CoefficientList[Series[-1 + 2*Sum[x^(k^2) * Product[(1 + x^(2*j - 1))/(1 - x^(2*j - 1)), {j, 1, k}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 12 2019 *)

Prog

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

Crossrefs

Other '8th-order' mock theta functions are at A153148, A153149, A153155, A153156, A153172, A153174, A153178.

Sequence in context: A023847 A279667 A000061 * A229144 A263021 A112921

Adjacent sequences: A153173 A153174 A153175 * A153177 A153178 A153179

Keyword

nonn

Author

Jeremy Lovejoy, Dec 20 2008

Extensions

More terms from Michel Marcus, Feb 23 2015

Status

approved