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 A109153 Column 0 of triangle A109152. 5

%I #4 Mar 30 2012 18:36:49

%S 1,1,2,6,22,94,450,2366,13450,81802,527826,3590294,25609782,190753502,

%T 1478339866,11884997478,98859026322,848881803218,7509881820930,

%U 68330806392070,638444805545622,6117166765086366,60028033370994386

%N Column 0 of triangle A109152.

%C 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.

%F 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.

%o (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])}

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Jun 20 2005

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Last modified July 13 08:08 EDT 2024. Contains 374274 sequences. (Running on oeis4.)