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A058643 McKay-Thompson series of class 35a for Monster. 0

%I #27 Jan 22 2023 09:36:46

%S 1,0,1,-1,1,1,0,0,-1,2,2,0,1,-2,1,3,0,1,-2,3,5,0,2,-3,3,6,0,2,-5,5,8,

%T 0,5,-7,6,12,0,5,-8,10,16,0,7,-12,13,21,0,9,-15,16,28,0,12,-20,21,36,

%U 0,14,-25,27,46,0,20,-34,34,58,0,24,-41,44,75,0,33,-54

%N McKay-Thompson series of class 35a for Monster.

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

%F G.f. is a period 1 Fourier series which satisfies f(-1 / (175 t)) = f(t) where q = exp(2 Pi i t). - _Michael Somos_, Jan 22 2023

%F Expansion of ( eta(q^35)^2 *(eta(q)^2 + 5*eta(q^25)^2) - eta(q^5)^2 *(5*eta(q^175)^2 +eta(q^7)^2) + eta(q)*eta(q^35)*(5*eta(q^25)*eta(q^35) + eta(q^5)*eta(q^7)) - 5*eta(q^5)*eta(q^175)*(eta(q^25)*eta(q^35) +eta(q^5)*eta(q^7)) )/(eta(q^5)*eta(q^35)*(5*eta(q^25)*eta(q^175) - eta(q)*eta(q^7)) in powers of q. - _Michael Somos_, Jan 22 2023

%e T35a = 1/q + q - q^2 + q^3 + q^4 - q^7 + 2*q^8 + 2*q^9 + q^11 - 2*q^12 + ...

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

%K sign

%O -1,10

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

%E More terms from _Georg Fischer_ using a PARI program of _Michael Somos_, Jan 21 2023

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)