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A053284 Coefficients of the '10th-order' mock theta function chi(q). 4

%I

%S 0,1,-1,1,-2,2,-1,2,-3,3,-3,3,-4,4,-4,5,-6,7,-6,7,-9,8,-8,10,-12,13,

%T -13,13,-16,17,-16,19,-21,22,-23,25,-28,29,-30,33,-37,39,-39,42,-48,

%U 49,-50,55,-60,64,-66,70,-77,81,-82,89,-97,101,-105,112,-121,126,-131,140,-151,159,-163,173,-187,194,-202

%N Coefficients of the '10th-order' mock theta function chi(q).

%D Youn-Seo Choi, Tenth order mock theta functions in Ramanujan's lost notebook, Inventiones Mathematicae, 136 (1999) 497-569

%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, p. 9

%H Vaclav Kotesovec, <a href="/A053284/b053284.txt">Table of n, a(n) for n = 0..10000</a> (corrected and extended previous b-file from G. C. Greubel)

%F G.f.: chi(q) = Sum_{n >= 0} (-1)^n q^(n+1)^2/((1+q)(1+q^2)...(1+q^(2n+1))).

%F a(n) ~ -(-1)^n * sqrt(phi) * exp(Pi*sqrt(n/10)) / (2*5^(1/4)*sqrt(n)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - _Vaclav Kotesovec_, Jun 12 2019

%t Series[Sum[(-1)^n q^(n+1)^2/Product[1+q^k, {k, 1, 2n+1}], {n, 0, 9}], {q, 0, 100}]

%t nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^((k+1)^2)/Product[1+x^j, {j, 1, 2*k+1}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 11 2019 *)

%Y Other '10th-order' mock theta functions are at A053281, A053282, A053283.

%K sign,easy

%O 0,5

%A _Dean Hickerson_, Dec 19 1999

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Last modified September 22 21:04 EDT 2021. Contains 347608 sequences. (Running on oeis4.)