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A007262 McKay-Thompson series of class 6c for Monster.
(Formerly M4078)
6

%I M4078 #43 Aug 22 2021 13:43:19

%S 1,-6,9,16,-66,54,98,-300,243,364,-1128,828,1221,-3498,2511,3528,

%T -9876,6804,9358,-25428,17217,23068,-61644,40824,53916,-141318,92340,

%U 119912,-310554,199980,256792,-656436,418311,530960,-1344144,847584,1066157,-2673372,1671741,2084464,-5186118,3216834,3981926,-9832752,6057504,7445924,-18269124,11181636,13661725,-33315852,20274948,24630344,-59740716

%N McKay-Thompson series of class 6c for Monster.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Seiichi Manyama, <a href="/A007262/b007262.txt">Table of n, a(n) for n = 0..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 G.f.: (E(q^2)/E(q^6))^6 / q where E(q) = Product_{n>=1} (1 - q^n); note that every second term is zero and is omitted in this sequence, cf. the PARI/GP code. - _Joerg Arndt_, Apr 09 2016

%e T6c = 1/q - 6*q + 9*q^3 + 16*q^5 - 66*q^7 + 54*q^9 + 98*q^11 - 300*q^13 + ...

%t eta[q_] := q^(1/24)*QP0chhammer[q]; a[n_]:= SeriesCoefficient[ q^(-1)*(eta[q^2]/ eta[q^6])^6, {q, 0, n}]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Jan 25 2018 *)

%o (PARI) N=66; q='q+O('q^N); Vec( (eta(q^1)/eta(q^3))^6/q ) \\ _Joerg Arndt_, Apr 09 2016

%Y Cf. A132107.

%K sign

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Joerg Arndt_, Apr 09 2016

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Last modified March 29 08:48 EDT 2024. Contains 371268 sequences. (Running on oeis4.)