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A109471
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Cumulative sum of absolute values of coefficients of q^(2n) in the series expansion of Ramanujan's mock theta function f(q).
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1
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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
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OFFSET
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0,2
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LINKS
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Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
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FORMULA
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post, Aug 28 2005
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STATUS
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approved
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