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A058670 McKay-Thompson series of class 41A for Monster. 1
1, 0, 2, 2, 3, 4, 7, 8, 11, 14, 19, 22, 30, 36, 46, 56, 70, 84, 106, 124, 153, 182, 221, 260, 314, 368, 440, 516, 611, 712, 842, 976, 1145, 1326, 1547, 1784, 2075, 2386, 2761, 3168, 3651, 4178, 4802, 5478, 6272, 7144, 8155, 9264, 10550, 11956, 13579, 15362 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

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, 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 (G(q^41)*H(q) - q^8*H(q^41)*G(q))^2, in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jul 03 2018

a(n) ~ exp(4*Pi*sqrt(n/41)) / (sqrt(2) * 41^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 04 2018

EXAMPLE

T41A = 1/q + 2*q + 2*q^2 + 3*q^3 + 4*q^4 + 7*q^5 + 8*q^6 + 11*q^7 + 14*q^8 + ...

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]; b:= G[x^41]*H[x] - x^8*H[x^41]*G[x]; a:= CoefficientList[Series[b^2, {x, 0, 90}], x]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jul 03 2018 *)

CROSSREFS

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

Sequence in context: A328789 A086969 A014692 * A215367 A276526 A091605

Adjacent sequences:  A058667 A058668 A058669 * A058671 A058672 A058673

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Nov 27 2000

EXTENSIONS

More terms from Michel Marcus, Feb 20 2014

STATUS

approved

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)