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A053280 A '7th-order' mock theta function. 6
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 (list; graph; refs; listen; history; text; internal format)
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: A320536 A338336 A298783 * A289122 A025832 A320385

Adjacent sequences:  A053277 A053278 A053279 * A053281 A053282 A053283

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

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Last modified May 15 17:11 EDT 2021. Contains 343920 sequences. (Running on oeis4.)