A167018 - OEIS

%I #8 Sep 14 2024 16:46:49

%S 1,1,4,20,149,1491,18612,275856,4699180,89993827,1907644760,

%T 44253266889,1113845999245,30214252304871,878483783958444,

%U 27252652393849400,898540310823301994,31378570076570865074,1157108876622296079054

%N Column 2 of triangle T=A167015: a(n) = T(n+2,2) = [T^(n+2)](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 {a(n)=A167015(n+2,2)}

%Y Cf. A167015, A167016, A167017, A167019.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Oct 27 2009