0,8

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

J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.

G.f.: Product_{k>0} (1-x^(6k-3))^3/(1-x^(2k-1)). - Michael Somos Mar 17 2004

Expansion of q^(1/3)*eta(q^2)eta(q^3)^3/(eta(q)eta(q^6)^3) in powers of q. - Michael Somos Mar 05 2004

Expansion of q^(1/3)*c(q)/c(q^2) in powers of q where c() is a cubic AGM analog function. - Michael Somos Oct 17 2006

Given g.f. A(x), then B(x)= A(x^3)/x satisfies 0= f(B(x), B(x^2)) where f(u, v)= 2*u +v^2 -u^2*v. - Michael Somos Mar 17 2004

Given g.f. A(x), then B(x)= A(x^3)/x satisfies 0= f(B(x), B(x^3)) where f(u, v)= (1 -v +v^2)* u^3 -(4 +2*v +v^2)* v. - Michael Somos Aug 11 2007

Given g.f. A(x), then B(x)= A(x^3)/x satisfies 0= f(B(x), B(x^5)) where f(u, v)= u^6 +v^6 -u^5*v^5 +5*u^4*v^4 -20*u^3*v^3 +20*u^2*v^2 -16*u*v +5*u^2*v^5 +5*u^5*v^2 -10*u^4*v -10*u*v^4. - Michael Somos Aug 11 2007

Euler transform of period 6 sequence [ 1, 0, -2, 0, 1, 0, ...]. - Michael Somos Mar 05 2004

G.f. is a period 1 Fourier series which satisfies f(-1/ (18 t)) = 2 g(t) where q = exp(2 pi i t) and g() is g.f. for A128128.

Expansion of chi(-q^3)^3 / chi(-q) in powers of q where chi() is a Ramanaujan theta function.

T18D = 1/q + q^2 + q^5 - q^8 - q^11 + q^17 + 2*q^20 - 2*q^26 - 3*q^29 + ...

(PARI) a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=3; A=subst(A, x, x^3)/x; A=(x*A*(4+2*A+A^2)/(1-A+A^2))^(1/3)); polcoeff(A, n))

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^3+A)^3/ eta(x+A)/eta(x^6+A)^3, n))}

A062244(n) = (-1)^n * a(n). A132179(n) = a(2*n). A092848(n) = a(2*n+1). Convolution inverse of A092848.

Sequence in context: A071447 A063514 A082490 this_sequence A062244 A079957 A104513

Adjacent sequences: A062239 A062240 A062241 this_sequence A062243 A062244 A062245

sign

njas, Jun 30 2001