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%I #12 Jun 12 2019 09:52:12
%S 1,3,6,11,17,27,38,55,76,103,136,182,235,303,385,489,612,766,945,1166,
%T 1428,1742,2111,2557,3072,3686,4401,5246,6223,7371,8692,10236,12014,
%U 14074,16435,19171,22292,25884,29981,34677,40017,46122,53038,60920
%N Cumulative sum of absolute values of coefficients of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
%H Vaclav Kotesovec, <a href="/A109471/b109471.txt">Table of n, a(n) for n = 0..5000</a>
%F a(n) = Sum_{k=0..n} abs(A000039(k)). [corrected by _Joerg Arndt_, Feb 25 2018]
%F a(n) ~ sqrt(3/2) * exp(sqrt(n/3)*Pi) / Pi. - _Vaclav Kotesovec_, Jun 12 2019
%t 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 *)
%Y Cf. A000039, A000019, A053250, A053251, A053252, A053253, A053254, A053255, A064053.
%K easy,nonn
%O 0,2
%A _Jonathan Vos Post_, Aug 28 2005