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A107674 Matrix square of triangle A107671.

%I A107674 #12 Mar 11 2021 03:04:58
%S A107674 1,24,4,2268,135,9,461056,15936,448,16,160977375,3789250,69000,1125,
%T A107674 25,85624508376,1485395280,19994688,223560,2376,36,64363893844726,
%U A107674 862907827866,9138674195,79086196,596820,4459,49,64928246784463872
%N A107674 Matrix square of triangle A107671.
%C A107674 Column 0 is A107675.
%F A107674 Matrix diagonalization method: define the triangular matrix P by P(n, k) = ((n+1)^3)^(n-k)/(n-k)! for n >= k >= 0 and the diagonal matrix D by D(n, n) = n+1 for n >= 0; then T is given by T = P^-1*D^2*P.
%e A107674 Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
%e A107674             1;
%e A107674            24,          4;
%e A107674          2268,        135,        9;
%e A107674        461056,      15936,      448,     16;
%e A107674     160977375,    3789250,    69000,   1125,   25;
%e A107674   85624508376, 1485395280, 19994688, 223560, 2376, 36;
%e A107674   ...
%o A107674 (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^2*P)[n+1,k+1])}
%Y A107674 Cf. A006690, A107667, A107671, A107675, A107676.
%K A107674 nonn,tabl
%O A107674 0,2
%A A107674 _Paul D. Hanna_, Jun 07 2005