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

1, 1, 5, 54, 940, 22917, 722530, 28009490, 1289854644, 68827561580, 4176770296181, 284087018905946, 21406395137288400, 1770085307452770344, 159359206078637624790, 15516776721991034328250

Offset: 0

Author

Paul D. Hanna, Aug 24 2007

Keywords

• nonn

Comments

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.

Crossrefs

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

Programs

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)}

Formula

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