|
|
A007252
|
|
McKay-Thompson series of class 5B for the Monster group with a(0) = 0.
(Formerly M4599)
|
|
3
|
|
|
1, 0, 9, 10, -30, 6, -25, 96, 60, -250, 45, -150, 544, 360, -1230, 184, -675, 2310, 1410, -4830, 750, -2450, 8196, 4920, -16180, 2376, -7875, 25644, 15000, -48720, 7126, -22800, 73221, 42310, -134760, 19284, -61400, 194334, 110610, -349000, 49563, -155250, 486370
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
-1,3
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
|
|
FORMULA
|
Expansion of 6 + (eta(q) / eta(q^5))^6 in powers of q. - Michael Somos, Apr 30 2004
|
|
EXAMPLE
|
T5B = 1/q + 9*q + 10*q^2 - 30*q^3 + 6*q^4 - 25*q^5 + 96*q^6 + 60*q^7 - ...
|
|
MATHEMATICA
|
a[ n_] := SeriesCoefficient[ 6 + 1/q (QPochhammer[ q] / QPochhammer[ q^5])^6, {q, 0, n}]; (* Michael Somos, May 22 2013 *)
|
|
PROG
|
(PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( 6*x + (eta(x + A) / eta(x^5 + A))^6, n))}; /* Michael Somos, Apr 30 2004 */
(PARI) {a(n) = my(A, k); if( n<-1, 0, k = (sqrtint(40*n + 48) + 7)\10; A = x * (sum(i=-k, k, (-1)^i * x^((5*i^2 + 3*i)/2), x^2 * O(x^n)) / sum(i=-k, k, (-1)^i * x^((5*i^2 + i)/2), x^2 * O(x^n)))^5; polcoeff( 1/A - A - 5, n))}; /* Michael Somos, Apr 30 2004 */
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|