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A058762 McKay-Thompson series of class 87A for Monster. 1
1, 0, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 4, 3, 4, 5, 5, 5, 8, 7, 8, 10, 10, 11, 15, 14, 16, 19, 20, 21, 27, 26, 30, 35, 36, 39, 47, 47, 52, 60, 63, 68, 80, 81, 90, 101, 106, 114, 132, 135, 148, 165, 174, 187, 212, 219, 239, 264, 279, 299, 334, 348, 377, 414, 438 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,7

COMMENTS

Also McKay-Thompson series of class 87B for Monster. - Michel Marcus, Feb 24 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).

David A. Madore, Coefficients of Moonshine (McKay-Thompson) series, The Math Forum

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of (1/4)*( -3 - T29A(q) - T29A(q^2) + sqrt((3 + T29A(q) + T29A(q^2))^2 + 8*(T29A(q)*T29A(q^2) - 3)) ) in powers of q, where T29A(q) = A058611. - G. C. Greubel, Jul 01 2018

a(n) ~ exp(4*Pi*sqrt(n/87)) / (sqrt(2) * 87^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T87A = 1/q + q^2 + q^3 + q^4 + 2*q^5 + q^6 + 2*q^7 + 2*q^8 + 2*q^9 + 2*q^10 + ...

MATHEMATICA

QP := QPochhammer; nmax = 100; 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^29]*G[x] + x^6*H[x^29]*H[x]; T29A := -2 + A^2/x; T87A := (1/4)*( -3 - T29A - (T29A/.{x -> x^3}) + ((3 + T29A + (T29A/.{x -> x^3}))^2 + 8*( T29A*(T29A /. {x -> x^3}) - 3) + O[x]^nmax)^(1/2) ); a:= CoefficientList[Series[x*T87A, {x, 0, nmax}], x]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jul 01 2018 *)

CROSSREFS

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

Sequence in context: A231577 A277210 A304777 * A241314 A276056 A276060

Adjacent sequences:  A058759 A058760 A058761 * A058763 A058764 A058765

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 24 2014

STATUS

approved

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Last modified October 16 08:40 EDT 2018. Contains 316259 sequences. (Running on oeis4.)