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A185628 Triangle, read by rows, equal to the matrix cube of triangle A185620.

%I A185628 #5 Mar 30 2012 18:37:26
%S A185628 1,3,1,6,3,1,16,12,3,1,60,55,18,3,1,305,315,118,24,3,1,1988,2243,912,
%T A185628 205,30,3,1,15951,19378,8342,1995,316,36,3,1,153171,198363,89193,
%U A185628 22274,3708,451,42,3,1,1722693,2358860,1098552,283427,48863,6195,610,48,3,1,22296396,32060736
%N A185628  Triangle, read by rows, equal to the matrix cube of triangle A185620.
%e A185628  Triangle begins:
%e A185628 1;
%e A185628 3, 1;
%e A185628 6, 3, 1;
%e A185628 16, 12, 3, 1;
%e A185628 60, 55, 18, 3, 1;
%e A185628 305, 315, 118, 24, 3, 1;
%e A185628 1988, 2243, 912, 205, 30, 3, 1;
%e A185628 15951, 19378, 8342, 1995, 316, 36, 3, 1;
%e A185628 153171, 198363, 89193, 22274, 3708, 451, 42, 3, 1;
%e A185628 1722693, 2358860, 1098552, 283427, 48863, 6195, 610, 48, 3, 1;
%e A185628 22296396, 32060736, 15376126, 4070883, 720586, 94085, 9600, 793, 54, 3, 1; ...
%e A185628 This triangle equals the matrix cube, R^3, of triangle R = A185620, which begins:
%e A185628 1;
%e A185628 1, 1;
%e A185628 1, 1, 1;
%e A185628 1, 3, 1, 1;
%e A185628 1, 10, 5, 1, 1;
%e A185628 1, 42, 27, 7, 1, 1;
%e A185628 1, 226, 173, 52, 9, 1, 1;
%e A185628 1, 1525, 1330, 442, 85, 11, 1, 1;
%e A185628 1, 12555, 12134, 4345, 897, 126, 13, 1, 1; ...
%e A185628 where R^3 - R^2 + I equals R shifted left one column.
%o A185628  (PARI) {T(n, k)=local(A=Mat(1), B); for(m=1, n, 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+1, k+1])}
%Y A185628  Cf. A185620, A185624, A185629, A185630, A185631.
%K A185628 nonn,tabl
%O A185628 0,2
%A A185628 _Paul D. Hanna_, Sep 07 2011