A053278 A '7th-order' mock theta function.

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 10, 11, 11, 13, 13, 14, 15, 16, 17, 19, 19, 21, 22, 24, 25, 28, 29, 31, 32, 35, 36, 40, 41, 44, 46, 49, 51, 56, 58, 62, 65, 69, 72, 77, 80, 86, 90, 95, 99, 106, 110, 117, 122, 130, 135, 144, 149, 158

Offset

0,7

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, 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(Pi/7) * sqrt(7*n)). - Vaclav Kotesovec, Jun 14 2019

Mathematica

Series[Sum[q^(7n(n-1))/Product[1-q^Abs[7k+1], {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+1], {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, A053279, A053280.

Sequence in context: A173711 A236678 A029378 * A035466 A122521 A086394

Adjacent sequences: A053275 A053276 A053277 * A053279 A053280 A053281

Keyword

nonn,easy

Author

Dean Hickerson, Dec 19 1999

Status

approved