0,2

McKay-Thompson series of class 12J for the Monster group.

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

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

J. McKay and H. Strauss, The q-series of monstrous moonshine and the decomposition of the head characters. Comm. Algebra 18 (1990), no. 1, 253-278.

T. J. I'a. Bromwich, Introduction to the Theory of Infinite Series, Macmillan, 2nd. ed. 1949, p. 116, q_2^4.

Index entries for McKay-Thompson series for Monster simple group

Expansion of chi(-q)^4 in powers of q where chi() is a Ramanujan theta function.

Expansion of q^(1/6) * (eta(q) / eta(q^2))^4 in powers of q.

Euler transform of period 2 sequence [ -4, 0, ...]. - Michael Somos Apr 26 2008

Given G.f. A(x) then B(x) = (A(x^6) / x)^2 satisfies 0 = f(B(x), B(x^2)) where f(u, v) = u * (16 + u * v) - v^2. - Michael Somos Apr 26 2008

Given G.f. A(x) then B(x) = A(x^6) / x satisfies 0 = f(B(x), B(x^2), B(x^4)) where f(u, v, w) = 4 * v * (v + u^2) - w^2 * (v - u^2). - Michael Somos Apr 26 2008

G.f. is a period 1 Fourier series which satisfies f(-1/(72 t)) = 4 / f(t) where q = exp(2 pi i t).

T12J = 1/q - 4q^5 + 6q^11 - 8q^17 + 17q^23 - 28q^29 + 38q^35 + ...

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x+A)/eta(x^2+A))^4, n))}

Convolution inverse of A022569.

Sequence in context: A049421 A039624 A083166 this_sequence A112160 A132040 A114315

Adjacent sequences: A022596 A022597 A022598 this_sequence A022600 A022601 A022602

sign

N. J. A. Sloane (njas(AT)research.att.com).