A107674 - OEIS

%I #12 Mar 11 2021 03:04:58

%S 1,24,4,2268,135,9,461056,15936,448,16,160977375,3789250,69000,1125,

%T 25,85624508376,1485395280,19994688,223560,2376,36,64363893844726,

%U 862907827866,9138674195,79086196,596820,4459,49,64928246784463872

%N Matrix square of triangle A107671.

%C Column 0 is A107675.

%F 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 Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:

%e             1;

%e            24,          4;

%e          2268,        135,        9;

%e        461056,      15936,      448,     16;

%e     160977375,    3789250,    69000,   1125,   25;

%e   85624508376, 1485395280, 19994688, 223560, 2376, 36;

%e   ...

%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^2*P)[n+1,k+1])}

%Y Cf. A006690, A107667, A107671, A107675, A107676.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Jun 07 2005