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A053279 A '7th order' mock theta function. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A027350 A029327

Adjacent sequences:  A053276 A053277 A053278 * A053280 A053281 A053282

KEYWORD

nonn,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

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Last modified July 13 09:43 EDT 2020. Contains 335686 sequences. (Running on oeis4.)