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URL: https://oeis.org/A058570

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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
OFFSET
-1,3
COMMENTS
Also, McKay-Thompson series of class 23B for Monster. - Michel Marcus, Feb 18 2014
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
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. A134781 (same sequence except for n=0).
Sequence in context: A176003 A216880 A144730 * A134781 A127977 A100848
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved