A058736 McKay-Thompson series of class 62A for Monster.

1, 0, 1, 1, 2, 1, 3, 2, 5, 4, 6, 5, 9, 8, 12, 11, 17, 15, 23, 21, 31, 29, 39, 38, 53, 50, 67, 66, 87, 85, 111, 110, 141, 141, 177, 178, 223, 225, 277, 283, 346, 352, 427, 438, 527, 542, 645, 666, 792, 818, 962, 1000, 1170, 1216, 1416, 1476, 1711, 1786, 2057

Offset

-1,5

Comments

Also McKay-Thompson series of class 62B for Monster. - Michel Marcus, Feb 24 2014

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 (T31A(q) * T31A(q^2))^(1/3) in powers of q, where T31A(q) = A058628. - G. C. Greubel, Jun 29 2018

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

Example

T62A = 1/q + q + q^2 + 2*q^3 + q^4 + 3*q^5 + 2*q^6 + 5*q^7 + 4*q^8 + 6*q^9 + ...

Mathematica

QP := QPochhammer; nmax = 260; 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]; B3 := ( G[x^31]*H[x] - x^6*H[x^31]*G[x])^3; a:= CoefficientList[Series[(B3 * (B3 /. {x -> x^2}) + O[x]^nmax)^(1/3), {x, 0, 60}], 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: A246995 A238782 A378749 * A097451 A005916 A034392

Adjacent sequences: A058733 A058734 A058735 * A058737 A058738 A058739

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 24 2014

Status

approved