A102087 Column 1 of triangular matrix A102086, which shifts upward to exclude the main diagonal under matrix square.

0, 2, 4, 20, 156, 1664, 22684, 378572, 7504640, 172785512, 4540756252, 134330010172, 4423176368332, 160596613105384, 6378859853838480, 275308217428662672, 12836003750434047344, 643227594173121801096

Offset: 0

Author

Paul D. Hanna, Dec 29 2004

Keywords

• nonn

Crossrefs

Cf. A102086, A102088.

Programs

Mathematica

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 *)

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])}