A132614 Column 1 of triangle A132610 divided by row index less one.

1, 2, 13, 162, 3093, 80540, 2669415, 107660354, 5120654779, 280715282502, 17430145081600, 1209171149737470, 92693370560208210, 7781500380680157240, 710001855526865191083, 69962579484461463387330

Offset: 1

Author

Paul D. Hanna, Aug 23 2007

Keywords

• nonn

Comments

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.

Crossrefs

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

Programs

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)}

Formula

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