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A058486 McKay-Thompson series of class 12H for Monster. 3
1, 0, 14, 36, 85, 180, 360, 684, 1246, 2196, 3754, 6264, 10226, 16380, 25804, 40032, 61275, 92628, 138452, 204804, 300040, 435672, 627356, 896400, 1271525, 1791324, 2507426, 3488472, 4825531, 6638688, 9085888, 12373992, 16772908, 22633812 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. A. Edgar, Table of n, a(n) for n = -1..1002

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Given g.f. A(x), then B(x) = A(x)+4 satisfies 0 = f(B(x), B(x^2)) where f(u, v) = -u*v*(1 + u^2*v^2) + 7*u*v*(u + v)*(1 + u*v) + 9*u*v*(u^2 + v^2). - Michael Somos, May 16 2004

Expansion of (eta(q^3) * eta(q^4) / (eta(q) * eta(q^12)))^4 - 4 in powers of q. - Michael Somos, May 16 2004

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 11 2016

EXAMPLE

T12H = 1/q + 14*q + 36*q^2 + 85*q^3 + 180*q^4 + 360*q^5 + 684*q^6 + ...

MATHEMATICA

QP = QPochhammer; s = (QP[q^3]*(QP[q^4]/(QP[q]*QP[q^12])))^4 - 4*q + O[q]^40; CoefficientList[s, q] (* Jean-Fran├žois Alcover, Nov 13 2015, adapted from PARI *)

PROG

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( (eta(x^3 + A) * eta(x^4 + A) / (eta(x + A) * eta(x^12 + A)))^4 - 4*x, n))}; /* Michael Somos, May 16 2004 */

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^6 * eta(x^6 + A)^6 / (eta(x + A)^5 * eta(x^3 + A) * eta(x^4 + A) * eta(x^12 + A)^5) - 5*x, n))}; /* Michael Somos, May 16 2004 */

CROSSREFS

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A177722 A165761 A165765 * A279900 A263125 A113627

Adjacent sequences:  A058483 A058484 A058485 * A058487 A058488 A058489

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

STATUS

approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)