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A058745 McKay-Thompson series of class 70B for Monster. 1

%I

%S 1,0,0,-1,1,0,0,0,0,-1,1,-1,2,-2,2,-1,1,-2,1,-1,3,-2,2,-4,3,-2,3,-4,4,

%T -4,5,-6,6,-7,6,-4,7,-8,5,-8,12,-11,12,-14,13,-12,13,-14,13,-14,19,

%U -21,20,-24,24,-22,27,-27,23,-30,37,-34,35,-40,42,-40,41

%N McKay-Thompson series of class 70B for Monster.

%H G. C. Greubel, <a href="/A058745/b058745.txt">Table of n, a(n) for n = -1..1000</a>

%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 David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1602206&amp;messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum

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

%F Expansion of 1 + eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/(eta(q^2)*eta(q^5) *eta(q^7)*eta(q^70)) in powers of q. - _G. C. Greubel_, Jun 30 2018

%F a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/35)) / (2 * 35^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 10 2018

%e T70B = 1/q - q^2 + q^3 - q^8 + q^9 - q^10 + 2*q^11 - 2*q^12 + 2*q^13 - q^14 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; B:= eta[q]*eta[q^10]*eta[q^14]* eta[q^35]/(eta[q^2]*eta[q^5]*eta[q^7]*eta[q^70]); a:= CoefficientList[ Series[q*(1 + B), {q, 0, 105}], q]; Table[a[[n]], {n, 1, 100}] (* _G. C. Greubel_, Jun 30 2018 *)

%t nmax = 100; CoefficientList[x + Series[Product[(1 + x^(5*k))*(1 + x^(7*k))/((1 + x^k)*(1 + x^(35*k))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Jul 10 2018 *)

%o (PARI) q='q+O('q^50); F = 1 + eta(q)*eta(q^10)*eta(q^14)*eta(q^35)/(q* eta(q^2)*eta(q^5)*eta(q^7)*eta(q^70)); Vec(F) \\ _G. C. Greubel_, Jun 30 2018

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

%K sign

%O -1,13

%A _N. J. A. Sloane_, Nov 27 2000

%E More terms from _Michel Marcus_, Feb 24 2014

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Last modified February 18 06:19 EST 2019. Contains 320245 sequences. (Running on oeis4.)