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Column 1 of triangle A185628.
3

%I #8 Mar 30 2012 18:37:26

%S 1,3,12,55,315,2243,19378,198363,2358860,32060736,491393909,

%T 8398281337,158541018923,3279307650137,73808041476439,

%U 1796794875356409,47063878147374980,1320276655048586177,39504980013582635300,1256210676237601811305,42313074100060933324771

%N Column 1 of triangle A185628.

%C Triangle A185628 equals the matrix cube of triangle R = A185620, which satisfies: R^3 - R^2 + I = R shifted left one column.

%o (PARI) {a(n)=local(A=Mat(1), B); for(m=1, n+2, B=A^3-A^2+A^0; A=matrix(m+1, m+1); for(i=1, m+1, for(j=1, i, if(i<2|j==i, A[i, j]=1, if(j==1, A[i, j]=1, A[i, j]=B[i-1, j-1]))))); return((A^3)[n+2, 2])}

%Y Cf. A185620, A185628, A185629, A185631.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Sep 07 2011