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%I #2 Mar 30 2012 18:37:05
%S 1,1,1,2,2,1,12,12,6,1,240,240,120,24,1,18480,18480,9360,2040,120,1,
%T 6708240,6708240,3466080,801360,55440,720,1,14088352320,14088352320,
%U 7423763760,1792667520,136972080,2202480,5040,1,203200845886080
%N Triangle, read by rows, where row n of T = row n-1 of T^n (shift right 1 column) with T(n,0)=T(n,1) for n>0.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 2, 1;
%e 12, 12, 6, 1;
%e 240, 240, 120, 24, 1;
%e 18480, 18480, 9360, 2040, 120, 1;
%e 6708240, 6708240, 3466080, 801360, 55440, 720, 1;
%e 14088352320, 14088352320, 7423763760, 1792667520, 136972080, 2202480, 5040, 1;
%e Matrix square T^2 begins:
%e 1;
%e 2, 1; <-- row 2 of T
%e 6, 4, 1;
%e 48, 36, 12, 1;
%e 1248, 1008, 384, 48, 1;
%e 127440, 108960, 45360, 6960, 240, 1; ...
%e Matrix cube T^3 begins:
%e 1;
%e 3, 1;
%e 12, 6, 1; <-- row 3 of T
%e 120, 72, 18, 1;
%e 3840, 2592, 792, 72, 1;
%e 486720, 359280, 125280, 14760, 360, 1; ...
%e Matrix fourth-power T^4 begins:
%e 1;
%e 4, 1;
%e 20, 8, 1;
%e 240, 120, 24, 1; <-- row 4 of T
%e 9120, 5280, 1344, 96, 1;
%e 1378560, 891840, 266400, 25440, 480, 1; ...
%o (PARI) {T(n,k)=local(M=if(n==0,[1],matrix(n+1,n+1,r,c,if(r>=c&r<=n,T(r-1,c-1))))); if(n==0,1,if(k==0,T(n,1),(M^n)[n,k]))}
%Y Cf. A132987 (column 0).
%K nonn,tabl
%O 0,4
%A _Paul D. Hanna_, Sep 07 2007
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