A058496 McKay-Thompson series of class 13B for the Monster group.

1, 0, -1, 2, 1, 2, -2, 0, -2, -2, 1, 0, 0, 4, -1, -4, 6, 2, 4, -6, -2, -4, -4, 0, -1, 0, 11, -2, -11, 16, 6, 12, -14, -2, -12, -12, 3, -2, -2, 24, -5, -24, 34, 12, 25, -32, -6, -24, -22, 4, -3, -2, 51, -10, -50, 72, 27, 52, -64, -12, -50, -48, 10, -8, -4, 98

Offset

-1,4

Links

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

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

Expansion of 2 + ( eta(q) / eta(q^13) )^2 in powers of q. - Michael Somos, Jul 05 2012

G.f.: 2 + (1/x) * Product_{k>0} ((1 - x^k) / (1 - x^(13*k)))^2. - Michael Somos, Jul 05 2012

a(n) = A133099(n) unless n=0. - Michael Somos, Jul 05 2012

Example

T13B = 1/q - q + 2*q^2 + q^3 + 2*q^4 - 2*q^5 - 2*q^7 - 2*q^8 + q^9 + 4*q^12 - ...

Mathematica

QP = QPochhammer; s = 2*q+(QP[q]/QP[q^13])^2+O[q]^70; CoefficientList[s, q] (* Jean-François Alcover, Nov 13 2015, adapted from PARI *)
eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[2 + (eta[q] /eta[q^13])^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Feb 18 2018 *)

Prog

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x*O(x^n); polcoeff( (eta(x + A) / eta(x^13 + A))^2 + 2*x, n))} /* Michael Somos, Jul 05 2012 */

Crossrefs

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

Cf. A133099.

Sequence in context: A035216 A258587 A263548 * A137579 A337108 A108805

Adjacent sequences: A058493 A058494 A058495 * A058497 A058498 A058499

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Status

approved