A192433 Coefficients of a mock theta function.

1, 1, 2, 3, 4, 5, 7, 9, 12, 16, 19, 24, 31, 37, 46, 57, 68, 83, 101, 120, 143, 171, 202, 239, 283, 331, 388, 455, 529, 616, 716, 827, 957, 1105, 1270, 1460, 1676, 1918, 2193, 2506, 2854, 3248, 3695, 4191, 4752, 5382, 6082, 6870, 7752, 8732, 9829

Offset: 0

Author

Jeremy Lovejoy, Jun 30 2011

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000
• K. Bringmann, K. Hikami and J. Lovejoy, On the modularity of the unified WRT invariants of certain Seifert manifolds
• K. Bringmann, K. Hikami, and J. Lovejoy, On the modularity of the unified WRT invariants of certain Seifert manifolds, Adv. Appl. Math. 46 (2011), 86-93.

Crossrefs

Cf. A053251.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^k*Product[1 + x^j, {j, 1, 2*k}], {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 16 2025 *)

PARI

N=66; q='q+O('q^N); gf=sum(n=0,N,q^n*prod(k=1,2*n,1+q^k)); Vec(gf) \\ Joerg Arndt, Jul 01 2011

Formula

a(n) = A053251(2*n+1).

a(n) ~ exp(Pi*sqrt(n/3)) / (4*sqrt(2*n)). - Vaclav Kotesovec, Jun 12 2019