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%I #3 Mar 30 2012 18:36:49
%S 1,3,9,63,492,4545,46935,530562,6485211,84764205,1176089460,
%T 17217555903,264670166322,4255132537038,71307312415452,
%U 1242006842599569,22428783284638182,419022897322142115,8083317501072692514
%N Column 2 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+3,n+3));M=M^0;for(i=1,n, M=matrix(n+3,n+3,r,c,if(r>=c,if(r==c,1,if(r==c+1,c,(M^3)[r-1,c]))))); return(M[n+3,3])}
%Y Cf. A109155, A109282 (triangle), A109283 (column 0), A109284 (column 1), A109286 (row sums).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jun 24 2005
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