A058570 McKay-Thompson series of class 23A for Monster.

1, 0, 4, 7, 13, 19, 33, 47, 74, 106, 154, 214, 307, 417, 575, 772, 1045, 1379, 1837, 2394, 3135, 4048, 5232, 6686, 8560, 10840, 13737, 17273, 21701, 27086, 33783, 41890, 51893, 63969, 78748, 96536, 118196, 144146, 175561, 213122, 258327, 312202

Offset

-1,3

Comments

Also, McKay-Thompson series of class 23B for Monster. - Michel Marcus, Feb 18 2014

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 (F + 1)*(F^2 + 4)/F^2, where F = eta(q)*eta(q^23)/(eta(q^2)* eta(q^46)), in powers of q. - G. C. Greubel, Jun 14 2018

a(n) ~ exp(4*Pi*sqrt(n/23)) / (sqrt(2) * 23^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

Example

T23A = 1/q + 4*q + 7*q^2 + 13*q^3 + 19*q^4 + 33*q^5 + 47*q^6 + 74*q^7 + ...

Mathematica

nmax = 50; QP = QPochhammer; s = -x + Sum[x^(2*j^2 + j*k + 3*k^2), {j, -nmax, nmax}, {k, -nmax, nmax}]/(QP[x]*QP[x^23]) + O[x]^nmax; CoefficientList[s, x] (* Jean-François Alcover, Nov 15 2015, adapted from g.f. in A134781 *)
eta[q_] := q^(1/24)*QPochhammer[q]; e46A:= (eta[q]*eta[q^23]/(eta[q^2]* eta[q^46])); a[n_]:= SeriesCoefficient[(e46A + 1)*(4 + e46A^2)/(e46A)^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Feb 13 2018 *)

Prog

(PARI) q='q+O('q^50); F = eta(q)*eta(q^23)/(q*eta(q^2)* eta(q^46)); Vec((F+1)*(F^2+4)/F^2) \\ G. C. Greubel, Jun 14 2018

Crossrefs

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

Cf. A134781 (same sequence except for n=0).

Sequence in context: A176003 A216880 A144730 * A134781 A127977 A100848

Adjacent sequences: A058567 A058568 A058569 * A058571 A058572 A058573

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved