A053280 A '7th-order' mock theta function.

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, 8, 8, 10, 9, 10, 11, 12, 11, 14, 13, 15, 16, 17, 17, 20, 19, 21, 22, 24, 24, 27, 27, 30, 31, 33, 34, 38, 37, 41, 43, 46, 46, 51, 52, 56, 58, 62, 63, 69, 70, 75, 78, 83, 85, 92, 94

Offset

0,13

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)

Dean Hickerson, On the seventh order mock theta functions, Inventiones Mathematicae, 94 (1988) 661-677.

Formula

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)).

a(n) ~ exp(Pi*sqrt(2*n/21)) / (2^(3/2) * sin(3*Pi/7) * sqrt(7*n)). - Vaclav Kotesovec, Jun 14 2019

Mathematica

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

Crossrefs

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

Sequence in context: A347698 A338336 A298783 * A289122 A370809 A025832

Adjacent sequences: A053277 A053278 A053279 * A053281 A053282 A053283

Keyword

nonn,easy

Author

Dean Hickerson, Dec 19 1999

Status

approved