A058628 McKay-Thompson series of class 31A for Monster.

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

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 A341241 A300300

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