A109153 Column 0 of triangle A109152.

1, 1, 2, 6, 22, 94, 450, 2366, 13450, 81802, 527826, 3590294, 25609782, 190753502, 1478339866, 11884997478, 98859026322, 848881803218, 7509881820930, 68330806392070, 638444805545622, 6117166765086366, 60028033370994386

Offset

0,3

Comments

Triangular matrix T=A109152 satisfies: T(n,k) = [T^2](n-1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0.

Links

Table of n, a(n) for n=0..22.

Formula

T^(m+1) = SHIFT_UP(T^m - T^(m-1)) - D*T^(m-1) for all m where diagonal matrix D = [0, 1, 2, 3, ...] and SHIFT_UP shifts each column up 1 row.

Prog

(PARI) {a(n)=local(M=matrix(n+1, n+1)); M=M^0; for(i=1, n, M=matrix(n+1, n+1, r, c, if(r>=c, if(r==c, 1, if(r==c+1, c, (M^2)[r-1, c]))))); return(M[n+1, 1])}

Crossrefs

Cf. A109152 (triangle), A109154 (column 1), A109155 (column 2), A109156 (row sums).

Sequence in context: A317652 A150274 A109317 * A030453 A001861 A049526

Adjacent sequences: A109150 A109151 A109152 * A109154 A109155 A109156

Keyword

nonn

Author

Paul D. Hanna, Jun 20 2005

Status

approved