login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053269 Coefficients of the '6th order' mock theta function psi(q). 12
0, 1, -1, 1, -2, 3, -2, 2, -4, 5, -5, 5, -7, 9, -8, 9, -12, 14, -15, 16, -20, 23, -23, 25, -31, 36, -37, 40, -47, 54, -56, 60, -71, 79, -84, 91, -103, 115, -121, 131, -149, 164, -174, 188, -210, 232, -245, 264, -294, 321, -343, 368, -406, 443, -470, 505, -554, 602, -641, 687, -751, 813, -863, 925 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 4, 13

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)

George E. Andrews and Dean Hickerson, Ramanujan's "lost" notebook VII: The sixth order mock theta functions, Advances in Mathematics, 89 (1991) 60-105.

FORMULA

G.f.: psi(q) = Sum_{n >= 0} (-1)^n q^(n+1)^2 (1-q)*(1-q^3)...(1-q^(2n-1)) /((1+q)*(1+q^2)...(1+q^(2n+1))).

a(3*n + 1) =  A262614(n). a(3*n + 2) = - A263041(n). - Michael Somos, Apr 17 2016

a(n) ~ -(-1)^n * exp(Pi*sqrt(n/6)) / (2*sqrt(3*n)). - Vaclav Kotesovec, Jun 15 2019

MATHEMATICA

Series[Sum[(-1)^n q^(n+1)^2 Product[1-q^k, {k, 1, 2n-1, 2}]/Product[1+ q^k, {k, 1, 2n+1}], {n, 0, 9}], {q, 0, 100}]

nmax = 100; CoefficientList[Series[Sum[(-1)^k * x^((k+1)^2) * Product[1-x^j, {j, 1, 2*k-1, 2}]/Product[1+ x^j, {j, 1, 2*k+1}], {k, 0, Floor[Sqrt[nmax]]}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 15 2019 *)

CROSSREFS

Other '6th order' mock theta functions are at A053268, A053270, A053271, A053272, A053273, A053274.

Cf. A262614, A263041.

Sequence in context: A287707 A029247 A194020 * A163873 A309563 A292588

Adjacent sequences:  A053266 A053267 A053268 * A053270 A053271 A053272

KEYWORD

sign,easy

AUTHOR

Dean Hickerson, Dec 19 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 9 14:08 EDT 2020. Contains 335543 sequences. (Running on oeis4.)