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%I #6 Mar 30 2012 18:36:46
%S 1,56,8,7965,513,27,2128064,81856,2368,64,914929500,23846125,469625,
%T 7625,125,576689214816,10943504136,160767720,1898856,19656,216,
%U 500750172337212,7250862593527,83548607478,776598305,6081733,43561,343
%N Matrix cube of triangle A107671.
%C Column 0 is A006690.
%F 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 Triangle begins:
%e 1;
%e 56,8;
%e 7965,513,27;
%e 2128064,81856,2368,64;
%e 914929500,23846125,469625,7625,125;
%e 576689214816,10943504136,160767720,1898856,19656,216; ...
%e which equals the matrix cube of triangle A107671:
%e 1;
%e 8,2;
%e 513,27,3;
%e 81856,2368,64,4;
%e 23846125,469625,7625,125,5;
%e 10943504136,160767720,1898856,19656,216,6; ...
%o (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 Cf. A107667, A107671, A107674, A006690.
%K nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Jun 07 2005
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