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Search: id:A107674
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| 1, 24, 4, 2268, 135, 9, 461056, 15936, 448, 16, 160977375, 3789250, 69000, 1125, 25, 85624508376, 1485395280, 19994688, 223560, 2376, 36, 64363893844726, 862907827866, 9138674195, 79086196, 596820, 4459, 49, 64928246784463872
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column 0 is A107675.
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FORMULA
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Matrix diagonalization method: define triangular matrix P by P(n, k) = ((n+1)^3)^(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
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Triangle begins:
1;
24,4;
2268,135,9;
461056,15936,448,16;
160977375,3789250,69000,1125,25;
85624508376,1485395280,19994688,223560,2376,36; ...
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PROGRAM
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(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])}
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CROSSREFS
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Cf. A107667, A107671, A107675, A107676, A082167.
Sequence in context: A040561 A040562 A040563 this_sequence A040560 A040558 A111803
Adjacent sequences: A107671 A107672 A107673 this_sequence A107675 A107676 A107677
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KEYWORD
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nonn,tabl
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 07 2005
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