|
| |
|
|
A145788
|
|
McKay-Thompson series of class 60C for the Monster group with a(0) = 2.
|
|
1
| |
|
|
1, 2, 1, 1, 2, 2, 2, 3, 5, 5, 5, 7, 9, 10, 11, 14, 18, 20, 22, 27, 32, 36, 40, 48, 57, 63, 70, 82, 95, 106, 119, 137, 158, 175, 195, 222, 252, 280, 311, 352, 397, 439, 486, 546, 611, 676, 747, 834, 929, 1024, 1128, 1253, 1389, 1528, 1679, 1857, 2052, 2250, 2467, 2718, 2993
(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 q^(-1) * (chi(q) * chi(q^15))^2 / (chi(q^3) * chi(q^5)) in powers of q where chi() is a Ramanujan theta function.
Expansion of (eta(q^2)^4 * eta(q^3) * eta(q^5) * eta(q^12) * eta(q^20) * eta(q^30)^4) / (eta(q) * eta(q^4) * eta(q^6) * eta(q^10) * eta(q^15) * eta(q^60))^2 in powers of q.
Euler transform of period 60 sequence.
G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = f(t) where q = exp(2 pi i t).
|
|
|
EXAMPLE
| 1/q + 2 + q + q^2 + 2*q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 5*q^7 + 5*q^8 + ...
|
|
|
PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^2 + A)^4 * eta(x^3 + A) * eta(x^5 + A) * eta(x^12 + A) * eta(x^20 + A) * eta(x^30 + A)^4) / (eta(x + A) * eta(x^4 + A) * eta(x^6 + A) * eta(x^10 + A) * eta(x^15 + A) * eta(x^60 + A))^2, n))}
|
|
|
CROSSREFS
| Convolution inverse of A145786. A145725(n) = A058727(n) = a(n) unless n=0. A133098(n) = -(-1)^n * a(n).
Sequence in context: A180234 A131059 A133098 * A117592 A117942 A066877
Adjacent sequences: A145785 A145786 A145787 * A145789 A145790 A145791
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Michael Somos, Oct 23 2008
|
| |
|
|
