A053279 A '7th-order' mock theta function.

1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 5, 6, 5, 7, 6, 8, 7, 9, 8, 10, 10, 11, 11, 13, 12, 15, 14, 17, 16, 19, 18, 21, 21, 23, 23, 27, 26, 30, 29, 33, 33, 37, 36, 41, 41, 46, 46, 51, 51, 56, 57, 62, 63, 69, 69, 77, 77, 84, 85, 93, 94, 102, 104, 112

Offset

0,11

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

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

Formula

G.f.: g(q^2, q^7), where g(x, q) = sum for n >= 1 of 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(2*Pi/7) * sqrt(7*n)). - Vaclav Kotesovec, Jun 14 2019

Mathematica

Series[Sum[q^(7n(n-1))/Product[1-q^Abs[7k+2], {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+2], {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, A053280.

Sequence in context: A265893 A191372 A185316 * A046800 A338718 A027350

Adjacent sequences: A053276 A053277 A053278 * A053280 A053281 A053282

Keyword

nonn,easy

Author

Dean Hickerson, Dec 19 1999

Status

approved