|
Search: id:A129588
|
|
|
| A129588 |
|
Expansion of q^-1 *theta_2(q)^4 in powers of q^2. |
|
+0
2
|
|
| 16, 64, 96, 128, 208, 192, 224, 384, 288, 320, 512, 384, 496, 640, 480, 512, 768, 768, 608, 896, 672, 704, 1248, 768, 912, 1152, 864, 1152, 1280, 960, 992, 1664, 1344, 1088, 1536, 1152, 1184, 1984, 1536, 1280, 1936, 1344, 1728, 1920, 1440
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
REFERENCES
|
K. Bobek, Einleitung in die Theorie der elliptischen Funktionen, Teubner Leipzig, 1884, p. 101.
|
|
FORMULA
|
G.f. sum{n>=0, a(n)*x^(2n+1) } = theta2(q)^4 = theta3(q)^4 - theta4(q)^4.
Expansion of 16*psi(q)^4 in powers of q where psi() is a Ramanujan theta function. - Michael Somos Jun 11 2007
Number of solutions of 2n+1 = (x^2+y^2+z^2+w^2)/4 in odd integers. - Michael Somos Jun 11 2007
G.f.: 16 * (Product_{k>0} (1-x^k)(1+x^k)^2)^4. - Michael Somos Jun 11 2007
|
|
PROGRAM
|
(PARI) {a(n)= if(n<0, 0, 16*sigma(2*n+1))} /* Michael Somos Jun 11 2007 */
|
|
CROSSREFS
|
a(n) = 16*A008438(n) = A000118(n)-A096727(n). Cf. A000122, A002448.
Adjacent sequences: A129585 A129586 A129587 this_sequence A129589 A129590 A129591
Sequence in context: A062320 A117453 A039370 this_sequence A043193 A043973 A153262
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ralf Stephan (ralf(AT)ark.in-berlin.de), May 30 2007
|
|
|
Search completed in 0.002 seconds
|
