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

0,2

Links

Table of n, a(n) for n=0..17.

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 *)

Prog

(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])}

Crossrefs

Cf. A102086, A102088.

Sequence in context: A303671 A330663 A370766 * A357671 A052573 A110371

Adjacent sequences: A102084 A102085 A102086 * A102088 A102089 A102090

Keyword

nonn

Author

Paul D. Hanna, Dec 29 2004

Status

approved