|
| |
|
|
A205977
|
|
McKay-Thompson series of class 30F for the Monster group with a(0) = 1.
|
|
1
|
|
|
|
1, 1, 3, 3, 8, 8, 16, 17, 33, 35, 59, 65, 105, 116, 175, 198, 292, 330, 466, 533, 736, 842, 1132, 1304, 1725, 1985, 2576, 2974, 3809, 4394, 5555, 6415, 8030, 9261, 11475, 13234, 16264, 18734, 22843, 26296, 31849, 36613, 44058, 50602, 60551, 69452, 82669
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
-1,3
|
|
|
LINKS
|
Table of n, a(n) for n=-1..45.
|
|
|
FORMULA
|
Expansion of eta(q^3) * eta(q^5) * eta(q^6) * eta(q^10) / (eta(q) * eta(q^2) * eta(q^15) * eta(q^30)) in powers of q.
Euler transform of period 30 sequence [ 1, 2, 0, 2, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 2, 1, 0, 1, 0, 0, 2, 1, 0, 0, 2, 0, 2, 1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (30 t)) = f(t) where q = exp(2 pi i t).
a(n) = A058617(n) unless n=0.
|
|
|
EXAMPLE
|
1/q + 1 + 3*q + 3*q^2 + 8*q^3 + 8*q^4 + 16*q^5 + 17*q^6 + 33*q^7 + ...
|
|
|
PROG
|
(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^3 + A) * eta(x^5 + A) * eta(x^6 + A) * eta(x^10 + A) / (eta(x + A) * eta(x^2 + A) * eta(x^15 + A) * eta(x^30 + A)), n))}
|
|
|
CROSSREFS
|
Cf. A058617.
Sequence in context: A168283 A135291 A058617 * A138135 A113166 A126872
Adjacent sequences: A205974 A205975 A205976 * A205978 A205979 A205980
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Michael Somos, Feb 02 2012
|
|
|
STATUS
|
approved
|
| |
|
|
