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A058742 McKay-Thompson series of class 68A for Monster. 1
1, 1, 1, 0, 2, 1, 3, 2, 4, 3, 6, 4, 7, 7, 10, 8, 14, 12, 18, 16, 23, 22, 30, 28, 39, 37, 49, 46, 62, 60, 78, 76, 97, 96, 122, 120, 150, 150, 185, 184, 228, 229, 278, 280, 338, 342, 410, 416, 495, 506, 597, 610, 718, 736, 859, 884, 1026, 1058, 1224, 1262, 1453, 1505, 1722, 1784, 2039 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,5

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..2500

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(T34A + 2), where T34A = A058638, in powers of q. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(2*Pi*sqrt(n/17)) / (2 * 17^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T68A = 1/q + q + q^3 + 2*q^7 + q^9 + 3*q^11 + 2*q^13 + 4*q^15 + 3*q^17 + ...

MATHEMATICA

QP := QPochhammer; nmax = 260; 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 := G[x^34]*G[x] + x^7*H[x^34]*H[x]; B:= G[x^17]*H[x^2] - x^3*H[x^17]*G[x^2]; T34A := -2 + (A*B)^2/x; a:= CoefficientList[Series[(x*(2 + T34A) + O[x]^nmax)^(1/2), {x, 0, 100}], x]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 29 2018 *)

CROSSREFS

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

Sequence in context: A265253 A161227 A115584 * A029140 A008584 A034390

Adjacent sequences:  A058739 A058740 A058741 * A058743 A058744 A058745

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

Terms a(12) onward added by G. C. Greubel, Jun 29 2018

STATUS

approved

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Last modified January 21 19:08 EST 2019. Contains 319350 sequences. (Running on oeis4.)