|
Search: id:A136569
|
|
|
| A136569 |
|
McKay-Thompson series of class 19A for the Monster group with a(0) = 3. |
|
+0
2
|
|
| 1, 3, 6, 10, 21, 36, 61, 96, 156, 232, 357, 522, 768, 1092, 1563, 2174, 3039, 4164, 5695, 7686, 10362, 13792, 18333, 24138, 31706, 41316, 53712, 69348, 89319, 114396, 146114, 185724, 235482, 297252, 374316, 469578, 587646, 732888, 911961, 1131250
(list; graph; listen)
|
|
|
OFFSET
|
-1,2
|
|
|
REFERENCES
|
K. Bringmann and H. Swisher, On a conjecture of Koike on identities between Thompson series and Roger-Ramanujan functions, Proc. Amer. Math. Soc. 135 (2007), 2317-2326. See page 2325 (A.5)
|
|
LINKS
|
Index entries for McKay-Thompson series for Monster simple group
|
|
FORMULA
|
G.f.: x^(-1) * ( G(x) * G(x^19) + x^4 * H(x) * H(x^19) )^3 where G() is g.f. of A003114 and H() is g.f. of A003106.
|
|
EXAMPLE
|
1/q + 3 + 6*q + 10*q^2 + 21*q^3 + 36*q^4 + 61*q^5 + 96*q^6 + 156*q^7 + ...
|
|
PROGRAM
|
(PARI) {a(n) = local(A, A1, A2); if( n<-1, 0, n = 2*n + 2 ; A = x^3 * O(x^n) ; A1 = ( eta(x + A) * eta(x^19 + A) / eta(x^2 + A) / eta(x^38 + A) )^2; A2 = -subst(A1, x, -x); A = ( x^4 / A1 / A2 - (A1 + A2) / 4 / x )^3; polcoeff( A, n ))}
|
|
CROSSREFS
|
Cf. A058549(n) = a(n) unless n=0.
Sequence in context: A068855 A068882 A076713 this_sequence A061883 A027671 A167617
Adjacent sequences: A136566 A136567 A136568 this_sequence A136570 A136571 A136572
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Michael Somos, Jan 07 2008
|
|
|
Search completed in 0.002 seconds
|
