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A034322
McKay-Thompson series of class 71A for Monster.
2
1, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4, 6, 6, 7, 8, 10, 11, 13, 14, 17, 19, 22, 24, 29, 31, 36, 40, 46, 50, 58, 63, 72, 79, 89, 98, 111, 121, 136, 149, 167, 182, 204, 222, 247, 270, 299, 326, 362, 393, 434, 473, 521, 566, 623, 676, 742, 806, 882, 956, 1047, 1133
OFFSET
-1,7
COMMENTS
Also McKay-Thompson series of class 71B for Monster. - Michel Marcus, Feb 19 2014
LINKS
I. Chen and N. Yui, Singular values of Thompson series. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.
J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum
FORMULA
a(n) ~ exp(4*Pi*sqrt(n/71)) / (sqrt(2) * 71^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 05 2018
EXAMPLE
T71A = 1/q + q + q^2 + q^3 + q^4 + 2*q^5 + 2*q^6 + 3*q^7 + 3*q^8 + 4*q^9 + ...
MATHEMATICA
QP := QPochhammer; f[x_, y_] := QP[-x, x*y]*QP[-y, x*y]*QP[x*y, x*y]; G[x_] := f[-x^2, -x^3]/f[-x, -x^2]; H[x_] := f[-x, -x^4]/f[-x, -x^2]; a:= CoefficientList[Series[G[x^71]*H[x] - x^14*H[x^71]*G[x], {x, 0, 80}], x]; Table[a[[n]], {n, 1, 70}] (* G. C. Greubel, Jul 05 2018 *)
CROSSREFS
KEYWORD
nonn
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved