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Column 0 of triangle T=A167015: a(n) = T(n,0) = [T^n](n-1,0) for n>0 with a(0)=1.
8

%I #6 Jul 27 2024 13:55:29

%S 1,1,2,9,70,755,10166,161350,2917524,58811631,1302452122,31362843270,

%T 814897356483,22712570157056,675859219349848,21387996239065027,

%U 717377276724961024,25427514619872897327,949918395837579798600

%N Column 0 of triangle T=A167015: a(n) = T(n,0) = [T^n](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,0)}

%Y Cf. A167015, A167017, A167018, A167019.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 27 2009