|
%I #6 Aug 17 2017 03:07:23
%S 1,3,3,0,-6,-9,0,15,21,0,-36,-45,0,78,96,0,-150,-189,0,276,342,0,-504,
%T -603,0,885,1050,0,-1488,-1773,0,2454,2901,0,-3996,-4662,0,6378,7404,
%U 0,-9972,-11565,0,15378,17748,0,-23472,-26910,0,35379,40413,0,-52644,-60021,0,77571,88152
%N 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.
%H G. C. Greubel, <a href="/A122831/b122831.txt">Table of n, a(n) for n = 0..1000</a>
%F 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.
%F Euler transform of period 18 sequence [ 3, -3, -1, -3, 3, 1, 3, -3, 0, -3, 3, 1, 3, -3, -1, -3, 3, 0, ...].
%t 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 *)
%o (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))}
%Y Cf. A122830(n)*3=a(n) if n>0.
%K sign
%O 0,2
%A _Michael Somos_, Sep 12 2006
|
