A109471 Cumulative sum of absolute values of coefficients of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).

1, 3, 6, 11, 17, 27, 38, 55, 76, 103, 136, 182, 235, 303, 385, 489, 612, 766, 945, 1166, 1428, 1742, 2111, 2557, 3072, 3686, 4401, 5246, 6223, 7371, 8692, 10236, 12014, 14074, 16435, 19171, 22292, 25884, 29981, 34677, 40017, 46122, 53038, 60920

Offset: 0

Author

Jonathan Vos Post, Aug 28 2005

Keywords

• easy
• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000039, A000019, A053250, A053251, A053252, A053253, A053254, A053255, A064053.

Programs

Mathematica

nmax = 200; f[q_, s_] := Sum[q^(n^2)/Product[1 + q^k, {k, n}]^2, {n, 0, s}]; A000039:= CoefficientList[Series[f[q, nmax], {q, 0, nmax}], q][[1 ;; -1 ;; 2]]; Table[Sum[Abs[A000039[[k]]], {k,1,n}], {n,1,51}] (* G. C. Greubel, Feb 18 2018 *)

Formula

a(n) = Sum_{k=0..n} abs(A000039(k)). [corrected by Joerg Arndt, Feb 25 2018]

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