login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053253 Coefficients of the '3rd order' mock theta function omega(q) 8
1, 2, 3, 4, 6, 8, 10, 14, 18, 22, 29, 36, 44, 56, 68, 82, 101, 122, 146, 176, 210, 248, 296, 350, 410, 484, 566, 660, 772, 896, 1038, 1204, 1391, 1602, 1846, 2120, 2428, 2784, 3182, 3628, 4138, 4708, 5347, 6072, 6880, 7784, 8804, 9940, 11208, 12630 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

Leila A. Dragonette, Some asymptotic formulae for the mock theta functions of Ramanujan, Trans. Amer. Math. Soc., 72 (1952) 474-500

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 15, 17, 31

George N. Watson, The final problem: an account of the mock theta functions, J. London Math. Soc., 11 (1936) 55-80

LINKS

Table of n, a(n) for n=0..49.

FORMULA

G.f.: omega(q) = sum(n>=0, q^(2*n*(n+1))/((1-q)*(1-q^3)*...*(1-q^(2*n+1)))^2 )

G.f.: Sum_{k>=0} x^k/((1-x)(1-x^3)...(1-x^(2k+1))). - Michael Somos, Aug 18 2006

G.f.: (1 - G(0) )/(1-x) where G(k) = 1 - 1/(1-x^(2*k+1))/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 18 2013

MATHEMATICA

Series[Sum[q^(2n(n+1))/Product[1-q^(2k+1), {k, 0, n}]^2, {n, 0, 6}], {q, 0, 100}]

PROG

(PARI) {a(n)=local(A); if(n<0, 0, A=1+x*O(x^n); polcoeff( sum(k=0, (sqrtint(2*n+1)-1)\2, A*=(x^(4*k)/(1-x^(2*k+1))^2 +x*O(x^(n-2*(k^2-k))))), n))} /* Michael Somos, Aug 18 2006 */

(PARI) {a(n)=local(A); if(n<0, 0, n++; A=1+x*O(x^n); polcoeff( sum(k=0, n-1, A*=(x/(1-x^(2*k+1)) +x*O(x^(n-k)))), n))} /* Michael Somos, Aug 18 2006 */

CROSSREFS

Other '3rd order' mock theta functions are at A000025, A053250, A053251, A053252, A053254, A053255.

Cf. A095913(n)=a(n-3).

Sequence in context: A014977 A008583 * A095913 A102848 A134157 A237751

Adjacent sequences:  A053250 A053251 A053252 * A053254 A053255 A053256

KEYWORD

nonn,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 | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 26 07:08 EST 2014. Contains 250020 sequences.