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A132619 Column 1 of triangle A132615 divided by twice the row index less 1. 4

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

%S 1,1,5,54,940,22917,722530,28009490,1289854644,68827561580,

%T 4176770296181,284087018905946,21406395137288400,1770085307452770344,

%U 159359206078637624790,15516776721991034328250

%N Column 1 of triangle A132615 divided by twice the row index less 1.

%C Triangle T=A132615 is generated by odd matrix powers of itself such that row n+1 of T = row n of T^(2n-1) with appended '1' for n>=0 with T(0,0)=1.

%F a(n) = A132615(n+1,1)/(2n-1) = A132617(n)/(2n-1) for n>=1.

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

%Y Cf. A132615 (triangle); columns: A132616, A132617, A132618.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Aug 24 2007

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Last modified May 2 17:46 EDT 2024. Contains 372203 sequences. (Running on oeis4.)