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A107670
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Matrix square of triangle A107667.
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4
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1, 12, 4, 216, 45, 9, 5248, 816, 112, 16, 160675, 20225, 2200, 225, 25, 5931540, 632700, 58176, 4860, 396, 36, 256182290, 23836540, 1920163, 138817, 9408, 637, 49, 12665445248, 1048592640, 75683648, 4886464, 290816, 16576, 960, 64
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listen;
history;
text;
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Matrix diagonalization method: define the triangular matrix P by P(n, k) = ((n+1)^2)^(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.
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EXAMPLE
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Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
1;
12, 4;
216, 45, 9;
5248, 816, 112, 16;
160675, 20225, 2200, 225, 25;
5931540, 632700, 58176, 4860, 396, 36;
256182290, 23836540, 1920163, 138817, 9408, 637, 49;
...
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PROG
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(PARI) {T(n, k)=local(P=matrix(n+1, n+1, r, c, if(r>=c, (r^2)^(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])}
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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