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A053278 A '7th-order' mock theta function. 6
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 17 12:26 EDT 2021. Contains 345080 sequences. (Running on oeis4.)