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A045483 McKay-Thompson series of class 5B for the Monster group with a(0) = 1. 3

%I #25 Jun 02 2018 21:27:38

%S 1,1,9,10,-30,6,-25,96,60,-250,45,-150,544,360,-1230,184,-675,2310,

%T 1410,-4830,750,-2450,8196,4920,-16180,2376,-7875,25644,15000,-48720,

%U 7126,-22800,73221,42310

%N McKay-Thompson series of class 5B for the Monster group with a(0) = 1.

%H Seiichi Manyama, <a href="/A045483/b045483.txt">Table of n, a(n) for n = -1..1000</a>

%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H J. McKay and H. Strauss, <a href="http://dx.doi.org/10.1080/00927879008823911">The q-series of monstrous moonshine and the decomposition of the head characters</a>, Comm. Algebra 18 (1990), no. 1, 253-278.

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of 7 + (eta(q) / eta(q^5))^6 in powers of q. - _Michael Somos_, May 22 2013

%F a(n) = A007252(n) = A106248(n) unless n=0.

%F a(n) = A229793(n) - A078905(n) for n > 0. - _Seiichi Manyama_, Jan 01 2017

%e 1/q + 1 + 9*q + 10*q^2 - 30*q^3 + 6*q^4 - 25*q^5 + 96*q^6 + 60*q^7 - ...

%t a[ n_] := SeriesCoefficient[ 7 + 1/q (QPochhammer[ q] / QPochhammer[ q^5])^6, {q, 0, n}] (* _Michael Somos_, May 22 2013 *)

%o (PARI) q='q+O('q^30); a= 7 + (eta(q)/eta(q^5))^6/q; Vec(a) \\ _G. C. Greubel_, Jun 02 2018

%Y Cf. A007252, A106248 (same except for initial terms).

%K sign

%O -1,3

%A _N. J. A. Sloane_

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)