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A058776 McKay-Thompson series of class 119A for Monster. 1
1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 10, 10, 11, 12, 13, 13, 15, 16, 18, 18, 21, 21, 23, 24, 27, 28, 31, 33, 35, 37, 40, 42, 46, 48, 53, 55, 59, 62, 68, 71, 76, 81, 86, 90, 97, 102, 110, 115, 124, 129 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,13

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = -1..10000 (terms -1..2500 from G. C. Greubel)

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 + A*B/q in powers of q, where A = G(q^119)*G(q) + q^24*H(q^119)*H(q), B = G(q^17)*H(q^7) - q^2*H(q^17)*G(q^7), G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jul 01 2018

a(n) ~ exp(4*Pi*sqrt(n/119)) / (sqrt(2) * 119^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T119A = 1/q + q^3 + q^4 + q^5 + q^6 + q^7 + q^8 + q^9 + q^10 + 2*q^11 + q^12 + ...

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:= G[x^119]*G[x] + x^24*H[x^119]*H[x]; B:= G[x^17]*H[x^7] - x^2*H[x^17]*G[x^7]; a:= CoefficientList[Series[-x + A*B, {x, 0, 60}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

CROSSREFS

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

Sequence in context: A294107 A240874 A029379 * A233296 A029228 A029215

Adjacent sequences:  A058773 A058774 A058775 * A058777 A058778 A058779

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 19 2014

STATUS

approved

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Last modified October 22 21:09 EDT 2018. Contains 316505 sequences. (Running on oeis4.)