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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 is A006689. See triangle A107667 for more formulas.
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FORMULA
| Matrix diagonalization method: define triangular matrix P by P(n, k) = ((n+1)^2)^(n-k)/(n-k)!, n>=k>=0 and diagonal matrix D(n, n) = n+1, then T is given by T = P^-1*D^2*P.
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EXAMPLE
| Triangle 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
| (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
| Cf. A107667, A107668, A107669, A006689 (column 0).
Sequence in context: A002911 A038330 A144630 * A157782 A002679 A133208
Adjacent sequences: A107667 A107668 A107669 * A107671 A107672 A107673
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KEYWORD
| nonn,tabl
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 07 2005
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