A093067 McKay-Thompson series of class 24f for the Monster group with a(0) = -2.

1, -2, -1, 4, -3, -2, 11, -6, -11, 20, -15, -16, 43, -24, -32, 76, -48, -58, 144, -84, -97, 238, -144, -172, 398, -234, -279, 636, -372, -428, 1012, -582, -678, 1564, -906, -1028, 2389, -1362, -1576, 3560, -2046, -2320, 5290, -2988, -3407, 7700, -4371, -4928

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

Formula

Expansion of (eta(q) * eta(q^5) / (eta(q^3) * eta(q^15)))^2 in powers of q.

Euler transform of period 15 sequence [ -2, -2, 0, -2, -4, 0, -2, -2, 0, -4, -2, 0, -2, -2, 0, ...].

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^3 + v^3 - 4*u*v * (u + v) - u^2*v^2 - 9*u*v.

a(n) = A058589(n) unless n=0.

Example

G.f. = 1/q - 2 - q + 4*q^2 - 3*q^3 - 2*q^4 + 11*q^5 - 6*q^6 - 11*q^7 + ...

Mathematica

a[ n_] := SeriesCoefficient[ q^(-1) (QPochhammer[ q] QPochhammer[ q^5] / (QPochhammer[q^3] QPochhammer[q^15]))^2, {q, 0, n}] (* Michael Somos, Oct 23 2013 *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x*O(x^n); polcoeff( (eta(x + A) * eta(x^5 + A) / (eta(x^3 + A) * eta(x^15 + A)))^2, n))}
(PARI) {a(n) = local(A, u, v); if( n<-1, 0, A = 1/x; for(k=0, n, u = A + x * O(x^k); v = subst(u, x, x^2); A += x^k * polcoeff(u^3 + v^3 - 4*u*v*(u + v) - u^2*v^2 - 9*u*v, k-5) / 2); polcoeff(A, n))}

Crossrefs

Cf. A058509.

Sequence in context: A124731 A210658 A143122 * A098122 A159931 A159755

Adjacent sequences: A093064 A093065 A093066 * A093068 A093069 A093070

Keyword

sign

Author

Michael Somos, Mar 17 2004

Extensions

Edited for better readability and more coherence. - Michael Somos, Oct 23 2013

Status

approved