-1,16

M. Somos, A Remarkable eta-product Identity

Index entries for McKay-Thompson series for Monster simple group

Expansion of eta(q) * eta(q^12) * eta(q^15) * eta(q^20) / (eta(q^3) * eta(q^4) * eta(q^5) * eta(q^60)) in powers of q.

Expansion of F(q) * F(q^2) in powers of q^3 where F(q) is g.f. for A112215.

Euler transform of a period 60 sequence.

G.f. is a period 1 Fourier series which satisfies f(-1 / (60 t)) = 1 / f(t) where q = exp(2 pi i t).

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = (u^2 + v^2) * (1 + u + v) * (u + v + u*v) - u*v * (1+ 2*u + 2*v + u*v)^2.

G.f.: (x * Product_{k>0} P(30, x^k) * P(60, x^k))^(-1) where P(n, x) is the nth cyclotomic polynomial.

1/q - 1 - q + q^2 - q^6 + q^7 + q^8 - q^9 - q^10 + q^11 - q^13 + 2*q^14 + ...

(PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x + A) * eta(x^12 + A) * eta(x^15 + A) * eta(x^20 + A) / (eta(x^3 + A) * eta(x^4 + A) * eta(x^5 + A) * eta(x^60 + A)), n))}

Cf. A058728(n) = a(n) unless n=0. Convolution inverse of A143752.

Sequence in context: A099751 A159937 A058728 this_sequence A158950 A059581 A163542

Adjacent sequences: A143748 A143749 A143750 this_sequence A143752 A143753 A143754

sign

Michael Somos, Aug 31 2008