|
| |
|
|
A145740
|
|
McKay-Thompson series of class 20C for the Monster group with a(0) = -2.
|
|
1
| |
|
|
1, -2, 1, -2, 2, 2, -1, 0, -4, 2, 5, -2, 0, -8, 2, 8, -3, 2, -14, 6, 14, -6, 4, -24, 12, 24, -11, 4, -40, 16, 38, -16, 5, -62, 24, 60, -24, 10, -94, 40, 91, -38, 18, -144, 62, 136, -57, 24, -214, 88, 201, -82, 30, -308, 122, 288, -117, 48, -440, 180, 410, -168, 74, -624, 262, 578, -238, 96, -874, 356, 804
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| -1,2
|
|
|
COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
|
|
|
LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
|
|
|
FORMULA
| Expansion of (eta(q) * eta(q^4) * eta(q^10) / (eta(q^2) * eta(q^5) * eta(q^20)))^2 in powers of q.
G.f. is a period 1 Fourier series which satisfies f(-1 / (80 t)) = 5 / f(t) where q = exp(2 pi i t).
Expansion of q^(-1) * (psi(-q) / psi(-q^5))^2 in powers of q where psi() is a Ramanujan theta function.
|
|
|
EXAMPLE
| 1/q - 2 + q - 2*q^2 + 2*q^3 + 2*q^4 - q^5 - 4*q^7 + 2*q^8 + 5*q^9 + ...
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x + A) * eta(x^4 + A) * eta(x^10 + A) / (eta(x^2 + A) * eta(x^5 + A) * eta(x^20 + A)))^2, n))}
|
|
|
CROSSREFS
| A112159(n) = a(n) unless n=0. Convolution square of A145708. -2 * A138522(n) = a(2*n).
Sequence in context: A134997 A104605 A138516 * A180580 A026513 A106028
Adjacent sequences: A145737 A145738 A145739 * A145741 A145742 A145743
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Michael Somos, Oct 17 2008
|
| |
|
|
