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A058753 McKay-Thompson series of class 76a for Monster. 1
1, 0, 1, 1, 2, 1, 2, 1, 3, 3, 4, 3, 6, 4, 7, 6, 10, 8, 12, 11, 16, 14, 20, 18, 26, 23, 31, 30, 40, 37, 49, 46, 60, 58, 73, 71, 90, 87, 109, 107, 133, 130, 160, 157, 192, 190, 229, 229, 275, 274, 326, 328, 388, 390, 459, 463, 542, 550, 638, 649, 752, 764, 880, 899, 1031, 1054, 1204 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1500

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of sqrt(T38A), where T38A = A058657, in powers of q. - G. C. Greubel, Jun 24 2018

a(n) ~ exp(2*Pi*sqrt(n/19)) / (2 * 19^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

EXAMPLE

T76a = 1/q + q^3 + q^5 + 2*q^7 + q^9 + 2*q^11 + q^13 + 3*q^15 + 3*q^17 + ...

MATHEMATICA

nmax = 100; QP := QPochhammer; G[q_] := 1/(QP[q, q^5]*QP[q^4, q^5]); H[q_] := 1/(QP[q^2, q^5]*QP[q^3, q^5]); T19A := -3 + (G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q; T38A := -1/2 + (17/4 + T19A + (T19A /. {q -> q^2}) + O[q]^nmax)^(1/2);  a:= CoefficientList[Series[(q*T38A + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 24 2018 *)

CROSSREFS

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

Sequence in context: A030273 A029197 A029174 * A282249 A304746 A304748

Adjacent sequences:  A058750 A058751 A058752 * A058754 A058755 A058756

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 24 2018

STATUS

approved

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Last modified January 19 23:25 EST 2019. Contains 319319 sequences. (Running on oeis4.)