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

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

Table of n, a(n) for n=-1..72.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

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

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

Sequence in context: A216789 A097951 A256171 * A343748 A029368 A108483

Adjacent sequences: A058640 A058641 A058642 * A058644 A058645 A058646

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