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A058570 McKay-Thompson series of class 23A for Monster. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified January 16 23:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)