

A152954


McKayThompson series of class 9d for the Monster group with a(0) = 2.


0



1, 2, 3, 2, 0, 6, 5, 0, 3, 6, 0, 18, 12, 0, 21, 16, 0, 6, 27, 0, 60, 34, 0, 72, 51, 0, 24, 70, 0, 168, 101, 0, 183, 134, 0, 54, 182, 0, 411, 240, 0, 450, 322, 0, 138, 416, 0, 936, 544, 0, 981, 696, 0, 282, 902, 0, 1989, 1144, 0, 2070, 1462, 0, 597, 1832, 0, 4026, 2317, 0, 4098
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..67.


FORMULA

Expansion of F(q)  2  3 / F(q) in powers of q where F(q) = (eta(q^9)^2 / (eta(q^3) * eta(q^27)))^2.
G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (v  u^2) * (u  v^2) + 4 * (1 + u + v) * (u + v + u*v).
G.f. is a period 1 Fourier series which satisfies f(1 / (81 t)) = f(t) where q = exp(2 pi i t).
a(3*n) = 0 unless n = 0.


EXAMPLE

1/q  2  3*q + 2*q^2 + 6*q^4 + 5*q^5 + 3*q^7 + 6*q^8  18*q^10 + 12*q^11 + ...


PROG

(PARI) {a(n) = local(A); if( n<1, 0, n++; A = x * O(x^n); A = (eta(x^9 + A)^2 / eta(x^3 + A) / eta(x^27 + A))^2; polcoeff( A  2 * x  3 * x^2 / A, n))}


CROSSREFS

A058096(n) = a(n) unless n = 0. a(3*n  1) = A058601(n).
Sequence in context: A076427 A011024 A105855 * A079175 A202815 A049336
Adjacent sequences: A152951 A152952 A152953 * A152955 A152956 A152957


KEYWORD

sign


AUTHOR

Michael Somos, Dec 15 2008


STATUS

approved



