A053280 - OEIS

%I #25 Jan 31 2021 20:47:01

%S 1,0,0,1,1,0,1,1,1,1,1,1,2,1,2,2,2,2,3,2,3,3,3,3,5,4,4,5,6,5,6,6,7,7,

%T 8,8,10,9,10,11,12,11,14,13,15,16,17,17,20,19,21,22,24,24,27,27,30,31,

%U 33,34,38,37,41,43,46,46,51,52,56,58,62,63,69,70,75,78,83,85,92,94

%N A '7th-order' mock theta function.

%H Vaclav Kotesovec, <a href="/A053280/b053280.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from G. C. Greubel)

%H Dean Hickerson, <a href="https://doi.org/10.1007/BF01394280">On the seventh order mock theta functions</a>, Inventiones Mathematicae, 94 (1988) 661-677.

%F G.f.: g(q^3, q^7), where g(x, q) = Sum_{n >= 1} q^(n(n-1))/((1-x)(1-q/x)(1-q x)(1-q^2/x)...(1-q^(n-1) x)(1-q^n/x)).

%F a(n) ~ exp(Pi*sqrt(2*n/21)) / (2^(3/2) * sin(3*Pi/7) * sqrt(7*n)). - _Vaclav Kotesovec_, Jun 14 2019

%t Series[Sum[q^(7n(n-1))/Product[1-q^Abs[7k+3], {k, -n, n-1}], {n, 1, 4}], {q, 0, 100}]

%t nmax = 100; CoefficientList[Series[Sum[x^(7*k*(k-1))/Product[1-x^Abs[7*j+3], {j, -k, k-1}], {k, 1, Floor[Sqrt[nmax/7]]+1}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jun 14 2019 *)

%Y Other '7th-order' mock theta functions are at A053275, A053276, A053277, A053278, A053279.

%K nonn,easy

%O 0,13

%A _Dean Hickerson_, Dec 19 1999