A132614 - OEIS

%I #2 Mar 30 2012 18:37:04

%S 1,2,13,162,3093,80540,2669415,107660354,5120654779,280715282502,

%T 17430145081600,1209171149737470,92693370560208210,

%U 7781500380680157240,710001855526865191083,69962579484461463387330

%N Column 1 of triangle A132610 divided by row index less one.

%C Triangle T=A132610 is generated by even matrix powers of itself such that row n+1 of T = row n of T^(2n) with appended '1' for n>=0 with T(0,0)=1.

%F a(n) = A132610(n+1,1)/n = A132612(n)/n for n>=1.

%o (PARI) {a(n)=local(A=vector(n+2), p); A[1]=1; if(n<1,0,for(j=1, n-1, p=n^2-(n-j)^2; A=Vec((Polrev(A)+x*O(x^p))/(1-x))); A=Vec((Polrev(A)+x*O(x^p))/(1-x)); A[p+1]/n)}

%Y Cf. A132610 (triangle); columns: A132611, A132612, A132613.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Aug 23 2007