1,11

Expansion of eta(q)eta(q^4)eta(q^7)eta(q^28)/(eta(q^2)eta(q^14)) in powers of q.

Euler transform of period 28 sequence [ -1, 0, -1, -1, -1, 0, -2, -1, -1, 0, -1, -1, -1, 0, -1, -1, -1, 0, -1, -1, -2, 0, -1, -1, -1, 0, -1, -2, ...].

Moebius transform is period 28 sequence [ 1, -2, -1, 0, -1, 2, 0, 0, 1, 2, 1, 0, -1, 0, 1, 0, -1, -2, -1, 0, 0, -2, 1, 0, 1, 2, -1, 0, ...].

Multiplicative with a(2^e) = -1 if e>0, a(7^e) = 1, a(p^e) = e+1 if p == 1, 2, 4 (mod 7), a(p^e) = (1+(-1)^e)/2 if p == 3, 5, 6 (mod 7).

G.f. A(x) satsifies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)= u^4*w*v +2*u^3*w*v^2 +2*u^2*w^2*v^2 +4*u^3*w^3 +4*u^3*w^2*v +8*u*w^4*v +8*u*w^3*v^2 +8*u^2*w^3*v -u^2*v^4 -2*u^2*w*v^3 -4*w^2*v^4 -4*u*w^2*v^3.

G.f.: Sum_{k>0} (-1)^k *x^k(1-x^(2k))(1-x^(4k))(1-x^(6k))/(1-x^(14k)) = x Product_{k>0} (1-x^k)(1+x^(2k))(1-x^(7k))(1+x^(14k)).

a(7n)=a(n). a(7n+3)=a(7n+5)=a(7n+6)=0.

(PARI) {a(n)=if(n<1, 0, -(-1)^n*sumdiv(n, d, kronecker(-28, d)))}

(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)*eta(x^7+A)*eta(x^28+A)/eta(x^2+A)/eta(x^14+A), n))}

a(n)=-(-1)^n*A035162(n).

Sequence in context: A087476 A033766 A035162 this_sequence A025462 A024879 A024316

Adjacent sequences: A121451 A121452 A121453 this_sequence A121455 A121456 A121457

sign,mult

Michael Somos, Jul 30 2006