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A058736 McKay-Thompson series of class 62A for Monster. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A123231 A246995 A238782 * 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

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Last modified January 18 03:13 EST 2019. Contains 319260 sequences. (Running on oeis4.)