A102087 - OEIS

%I #7 Dec 15 2014 05:17:54

%S 0,2,4,20,156,1664,22684,378572,7504640,172785512,4540756252,

%T 134330010172,4423176368332,160596613105384,6378859853838480,

%U 275308217428662672,12836003750434047344,643227594173121801096

%N Column 1 of triangular matrix A102086, which shifts upward to exclude the main diagonal under matrix square.

%t T[n_, n_] := n+1; T[n_, k_] /; k>n = 0; T[n_, k_] /; k == n-1 := n^2; T[n_, k_] := T[n, k] = Coefficient[1-Sum[T[i, k]*x^i*Product[1-(j+k)*x, {j, 1, i-k+1}], {i, k, n-1}], x, n]; a[n_] := T[n, 1]; Table[a[n], {n, 0, 17} ] (* _Jean-François Alcover_, Dec 15 2014 *)

%o (PARI) {a(n)=local(A=matrix(2,2),B);A[1,1]=1; for(m=2,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=j,if(j==1,B[i,j]=(A^2)[i-1,1], B[i,j]=(A^2)[i-1,j]));));A=B); return(A[n+1,2])}

%Y Cf. A102086, A102088.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Dec 29 2004