|
%I #24 Jun 12 2019 09:01:23
%S 1,2,3,4,6,8,11,14,18,24,30,38,47,58,72,88,108,130,156,188,225,268,
%T 318,376,444,522,612,716,834,972,1129,1308,1512,1744,2010,2310,2652,
%U 3038,3474,3968,4524,5152,5857,6650,7542,8540,9660,10912,12312,13878
%N Coefficients of the '6th-order' mock theta function rho(q).
%D Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 3, 13
%H Vaclav Kotesovec, <a href="/A053270/b053270.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from G. C. Greubel)
%H George E. Andrews and Dean Hickerson, <a href="https://doi.org/10.1016/0001-8708(91)90083-J">Ramanujan's "lost" notebook VII: The sixth order mock theta functions</a>, Advances in Mathematics, 89 (1991) 60-105.
%F G.f.: rho(q) = Sum_{n >= 0} ( q^(n(n+1)/2) *(1+q)*(1+q^2)...(1+q^n)/((1-q)*(1-q^3)...(1-q^(2n+1))) ).
%F a(n) ~ exp(Pi*sqrt(n/3)) / (2*sqrt(3*n)). - _Vaclav Kotesovec_, Jun 12 2019
%t Series[Sum[q^(n(n+1)/2) Product[1+q^k, {k, 1, n}]/Product[1-q^k, {k, 1, 2n+1, 2}], {n, 0, 13}], {q, 0, 100}]
%t nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2) * Product[1+x^j, {j, 1, k}]/Product[1-x^j, {j, 1, 2*k+1, 2}], {k, 0, Floor[Sqrt[2*nmax]]}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 12 2019 *)
%Y Other '6th-order' mock theta functions are at A053268, A053269, A053271, A053272, A053273, A053274.
%K nonn,easy
%O 0,2
%A _Dean Hickerson_, Dec 19 1999
|
