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

0,2

Links

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

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

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 *)

Crossrefs

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

Sequence in context: A003453 A011901 A169739 * A279032 A124454 A335631

Adjacent sequences: A109468 A109469 A109470 * A109472 A109473 A109474

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 28 2005

Status

approved