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A167017 Column 1 of triangle T=A167015: a(n) = T(n+1,1) = [T^(n+1)](n-1,0) for n>0 with a(0)=1. 4

%I #2 Mar 30 2012 18:37:20

%S 1,1,3,14,105,1080,13916,212634,3723198,73047825,1581256303,

%T 37350588290,954796686233,26246234745486,771853099673490,

%U 24180166328032252,803996438505301917,28283254774663359546,1049653570430645994556

%N Column 1 of triangle T=A167015: a(n) = T(n+1,1) = [T^(n+1)](n-1,0) for n>0 with a(0)=1.

%C In triangle T=A167015, row n of T equals the initial n terms in column 0 of matrix power T^n, reversed and with an appended '1'.

%o (PARI) {A167015(n,k)=local(M,N);if(n==k|n==k+1,1,if(n==k+2,k+2, N=matrix(n,n,r,c,if(r>=c,A167015(r-1,c-1))); M=matrix(n+1,n+1,r,c,if(r>=c,if(r<=n,N[r,c],(N^n)[n-k,1])));M[n+1,k+1]))}

%o (PARI) {a(n)=A167015(n+1,1)}

%Y Cf. A167015, A167016, A167018, A167019.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 27 2009

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