A109284 Column 1 of triangle A109282.

1, 2, 6, 36, 258, 2190, 20988, 222042, 2554890, 31606740, 416907618, 5824488540, 85725372240, 1323363947268, 21348018188394, 358735098433608, 6262471636627866, 113303272081250532, 2120102973225741564

Offset

0,2

Comments

Triangular matrix T=A109282 satisfies: T(n,k) = [T^3](n-1,k) for n>k+1>=1, with T(n,n) = 1 and T(n+1,n) = n+1 for n>=0; also, T^(m+3) = SHIFT_UP(T^(m+1) - T^m) - D*T^m for all m where diagonal matrix D = [0,1,2,3,...] and SHIFT_UP shifts each column up 1 row.

Links

Table of n, a(n) for n=0..18.

Prog

(PARI) {a(n)=local(M=matrix(n+2, n+2)); M=M^0; for(i=1, n, M=matrix(n+2, n+2, r, c, if(r>=c, if(r==c, 1, if(r==c+1, c, (M^3)[r-1, c]))))); return(M[n+2, 2])}

Crossrefs

Cf. A109154, A109282 (triangle), A109283 (column 0), A109285 (column 2), A109286 (row sums).

Sequence in context: A347897 A354413 A177373 * A060178 A096939 A351825

Adjacent sequences: A109281 A109282 A109283 * A109285 A109286 A109287

Keyword

nonn

Author

Paul D. Hanna, Jun 24 2005

Status

approved