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A058629 McKay-Thompson series of class 32A for Monster. 1
1, 0, 2, 4, 6, 8, 12, 16, 23, 32, 42, 56, 74, 96, 124, 160, 203, 256, 324, 404, 502, 624, 768, 944, 1156, 1408, 1710, 2072, 2500, 3008, 3612, 4320, 5157, 6144, 7296, 8648, 10232, 12072, 14220, 16720, 19616, 22976, 26868, 31360, 36546, 42528, 49404, 57312 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

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 A - 2, where A = (eta(q^2)*eta(q^16))^3/( eta(q)^2*eta(q^4) *eta(q^8)*eta(q^32)^2), in powers of q. - G. C. Greubel, Jun 23 2018

a(n) ~ exp(sqrt(n/2)*Pi) / (2^(7/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T32A = 1/q + 2*q + 4*q^2 + 6*q^3 + 8*q^4 + 12*q^5 + 16*q^6 + 23*q^7 + ...

MATHEMATICA

eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q^2]*eta[q^16])^3/( eta[q]^2*eta[q^4]*eta[q^8]*eta[q^32]^2); a:= CoefficientList[Series[ q*(-2 + A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

PROG

(PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^16))^3/( eta(q)^2*eta(q^4) *eta(q^8)*eta(q^32)^2)/q; Vec(A - 2) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

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

Sequence in context: A228354 A065386 A048951 * A323508 A095810 A025487

Adjacent sequences:  A058626 A058627 A058628 * A058630 A058631 A058632

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 January 22 05:11 EST 2019. Contains 319353 sequences. (Running on oeis4.)