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A058628 McKay-Thompson series of class 31A for Monster. 2
1, 0, 3, 3, 6, 9, 13, 18, 27, 34, 48, 63, 85, 108, 144, 181, 237, 297, 379, 471, 597, 733, 915, 1122, 1385, 1686, 2067, 2498, 3039, 3657, 4415, 5286, 6351, 7565, 9033, 10722, 12741, 15057, 17817, 20973, 24714, 28998, 34033, 39798, 46551, 54262, 63255, 73530 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

COMMENTS

Also McKay-Thompson series of class 31B for Monster.

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^31)*H(q) - q^6*H(q^31)*G(q))^3 in powers of q, where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 29 2018

Expansion of (T93A)^3 in powers of q, where T93A = A112217. - G. C. Greubel, Jun 29 2018

a(n) ~ exp(4*Pi*sqrt(n/31)) / (sqrt(2) * 31^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 29 2018

EXAMPLE

T31A = 1/q + 3*q + 3*q^2 + 6*q^3 + 9*q^4 + 13*q^5 + 18*q^6 + 27*q^7 + ...

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^31]*H[x] - x^6*H[x^31]*G[x]; a:= CoefficientList[Series[B^3, {x, 0, 50}], x]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 29 2018 *)

CROSSREFS

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

Sequence in context: A289143 A323451 A280240 * A035528 A300300 A293675

Adjacent sequences:  A058625 A058626 A058627 * A058629 A058630 A058631

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 October 14 15:03 EDT 2019. Contains 328019 sequences. (Running on oeis4.)