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A112196 McKay-Thompson series of class 56a for the Monster group. 1
1, 1, 1, 1, 3, 2, 2, 5, 6, 7, 7, 9, 12, 13, 16, 20, 25, 27, 31, 38, 44, 51, 58, 69, 80, 92, 102, 118, 141, 157, 177, 203, 234, 261, 292, 336, 382, 428, 475, 540, 610, 677, 757, 852, 957, 1060, 1179, 1318, 1470, 1634, 1806, 2011, 2236, 2469, 2724, 3020, 3350 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of sqrt(T28B + 2) in powers of q, where T28B = A112169. - G. C. Greubel, Jul 01 2018

a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jul 02 2018

EXAMPLE

T56a = 1/q +q +q^3 +q^5 +3*q^7 +2*q^9 +2*q^11 +5*q^13 +6*q^15 +...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 70; A:= (eta[q]*eta[q^7]/ (eta[q^4]*eta[q^28])); T28B := 1 + A + 4/A; a:= CoefficientList[Series[ (q*(T28B + 2) + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

PROG

(PARI) q='q+O('q^50); A = eta(q)*eta(q^7)/(q*eta(q^4)*eta(q^28)); T28B = A + 1 + 4/A; Vec(sqrt(q*(T28B + 2))) \\ G. C. Greubel, Jul 01 2018

CROSSREFS

Cf. A112169.

Sequence in context: A282161 A205675 A058608 * A021035 A259967 A007567

Adjacent sequences:  A112193 A112194 A112195 * A112197 A112198 A112199

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified January 20 17:05 EST 2019. Contains 319335 sequences. (Running on oeis4.)