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A058643
McKay-Thompson series of class 35a for Monster.
0
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, 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, 0, 14, -25, 27, 46, 0, 20, -34, 34, 58, 0, 24, -41, 44, 75, 0, 33, -54
OFFSET
-1,10
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
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
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
EXAMPLE
T35a = 1/q + q - q^2 + q^3 + q^4 - q^7 + 2*q^8 + 2*q^9 + q^11 - 2*q^12 + ...
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Georg Fischer using a PARI program of Michael Somos, Jan 21 2023
STATUS
approved