A122779 Expansion of F(q)*F(q^5) where F(q) = eta(q^2)*eta(q^3)^3 / (eta(q)*eta(q^6)).

1, 1, 1, -1, -1, 1, 0, 1, -3, -1, 0, -1, 2, -4, -1, -1, -2, 1, -4, 1, 0, 0, 4, 1, 1, 2, 5, 4, 2, -1, 0, 1, 0, 6, 0, -1, 2, -4, 2, -1, 2, -4, -8, 0, 3, 0, -4, -1, 1, 1, -2, -2, -6, 1, 0, -4, -4, -6, 8, 1, -2, 8, -8, -1, -2, 0, 0, -6, 4, 4, -8, 1, 2, 2, 1, 4, 0, 2, 8, 1, 1, -6, 8, 4, 2, -4, 2, 0, 2, -1, 0, 0, 0, 0, 4, 1, 2, 9, 0, -1, 10, 6, 8, 2, 0

Offset

1,9

Links

G. C. Greubel, Table of n, a(n) for n = 1..1500

Formula

Euler transform of period 30 sequence [ 1, 0, -2, 0, 2, -2, 1, 0, -2, 0, 1, -2, 1, 0, -4, 0, 1, -2, 1, 0, -2, 0, 1, -2, 2, 0, -2, 0, 1, -4, ...].

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; F[q_]:= eta[q^2]*eta[q^3]^3/(eta[q]*eta[q^6]); a:= CoefficientList[Series[F[q]*F[q^5], {q, 0, 100}], q]; Table[a[[n]], {n, 2, 50}] (* G. C. Greubel, Jul 18 2018 *)

Prog

(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); A=eta(x^2+A)*eta(x^3+A)^3/eta(x+A)/eta(x^6+A); A=A*subst(A+x*O(x^(n\5)), x, x^5); polcoeff(A, n))}

Crossrefs

A122777(n)=a(2n).

Sequence in context: A291635 A308243 A268386 * A120323 A320476 A304326

Adjacent sequences: A122776 A122777 A122778 * A122780 A122781 A122782

Keyword

sign

Author

Michael Somos, Sep 10 2006

Status

approved