A122831 Expansion of b(q^3)b(q^2)^2/(b(q)b(q^6)^2) in powers of q where b(q) is a cubic AGM function.

1, 3, 3, 0, -6, -9, 0, 15, 21, 0, -36, -45, 0, 78, 96, 0, -150, -189, 0, 276, 342, 0, -504, -603, 0, 885, 1050, 0, -1488, -1773, 0, 2454, 2901, 0, -3996, -4662, 0, 6378, 7404, 0, -9972, -11565, 0, 15378, 17748, 0, -23472, -26910, 0, 35379, 40413, 0, -52644, -60021, 0, 77571, 88152

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

Expansion of eta(q^2)^6*eta(q^3)^4*eta(q^18)^2/(eta(q)^3*eta(q^6)^8*eta(q^9)) in powers of q.

Euler transform of period 18 sequence [ 3, -3, -1, -3, 3, 1, 3, -3, 0, -3, 3, 1, 3, -3, -1, -3, 3, 0, ...].

Mathematica

eta[x_] := x^(1/24)*QPochhammer[x]; A122831[n_] := SeriesCoefficient[ eta[q^2]^6*eta[q^3]^4*eta[q^18]^2/(eta[q]^3*eta[q^6]^8*eta[q^9] ), {q, 0, n}]; Table[A122831[n], {n, 0, 50}] (* G. C. Greubel, Aug 17 2017 *)

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^6*eta(x^3+A)^4*eta(x^18+A)^2/eta(x+A)^3/eta(x^6+A)^8/eta(x^9+A), n))}

Crossrefs

Cf. A122830(n)*3=a(n) if n>0.

Sequence in context: A319256 A354618 A117234 * A019701 A134813 A338037

Adjacent sequences: A122828 A122829 A122830 * A122832 A122833 A122834

Keyword

sign

Author

Michael Somos, Sep 12 2006

Status

approved