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A107676 Matrix cube of triangle A107671.

%I A107676 #6 Mar 30 2012 18:36:46
%S A107676 1,56,8,7965,513,27,2128064,81856,2368,64,914929500,23846125,469625,
%T A107676 7625,125,576689214816,10943504136,160767720,1898856,19656,216,
%U A107676 500750172337212,7250862593527,83548607478,776598305,6081733,43561,343
%N A107676 Matrix cube of triangle A107671.
%C A107676 Column 0 is A006690.
%F A107676 Matrix diagonalization method: define triangular matrix P by P(n, k) = ((n+1)^3)^(n-k)/(n-k)!, n>=k>=0 and diagonal matrix D(n, n) = n+1, then T is given by T = P^-1*D^3*P.
%e A107676 Triangle begins:
%e A107676 1;
%e A107676 56,8;
%e A107676 7965,513,27;
%e A107676 2128064,81856,2368,64;
%e A107676 914929500,23846125,469625,7625,125;
%e A107676 576689214816,10943504136,160767720,1898856,19656,216; ...
%e A107676 which equals the matrix cube of triangle A107671:
%e A107676 1;
%e A107676 8,2;
%e A107676 513,27,3;
%e A107676 81856,2368,64,4;
%e A107676 23846125,469625,7625,125,5;
%e A107676 10943504136,160767720,1898856,19656,216,6; ...
%o A107676 (PARI) {T(n,k)=local(P=matrix(n+1,n+1,r,c,if(r>=c,(r^3)^(r-c)/(r-c)!)), D=matrix(n+1,n+1,r,c,if(r==c,r)));if(n>=k,(P^-1*D^3*P)[n+1,k+1])}
%Y A107676 Cf. A107667, A107671, A107674, A006690.
%K A107676 nonn,tabl
%O A107676 0,2
%A A107676 _Paul D. Hanna_, Jun 07 2005