|
%I #3 Mar 30 2012 18:36:49
%S 1,2,6,36,258,2190,20988,222042,2554890,31606740,416907618,5824488540,
%T 85725372240,1323363947268,21348018188394,358735098433608,
%U 6262471636627866,113303272081250532,2120102973225741564
%N Column 1 of triangle A109282.
%C 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.
%o (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])}
%Y Cf. A109154, A109282 (triangle), A109283 (column 0), A109285 (column 2), A109286 (row sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 24 2005
|
