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Search: id:A055137
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| A055137 |
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Regard triangle of rencontres numbers (see A008290) as infinite matrix, compute inverse, read by rows. |
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3
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| 1, 0, 1, -1, 0, 1, -2, -3, 0, 1, -3, -8, -6, 0, 1, -4, -15, -20, -10, 0, 1, -5, -24, -45, -40, -15, 0, 1, -6, -35, -84, -105, -70, -21, 0, 1, -7, -48, -140, -224, -210, -112, -28, 0, 1, -8, -63, -216, -420, -504, -378, -168, -36, 0, 1, -9, -80, -315, -720
(list; table; graph; listen)
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OFFSET
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0,7
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COMMENT
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The n-th row consists of coefficients of the characteristic polynomial of the adjacency matrix of the complete n-graph.
Triangle of coefficients of det(M(n)) where M(n) is the n X n matrix m(i,j)=x if i=j, m(i,j)=i/j otherwise. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 01 2003
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REFERENCES
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Norman Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. p. 17.
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FORMULA
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G.f.: (x-n+1)*(x+1)^(n-1) = sum T(n, k)x^k. T(n, k) = (1-n+k)*C(n, k).
k-th column has o.g.f. x^k(1-(k+2)x)/(1-x)^(k+2). k-th row gives coefficients of (x-k)(x+1)^k. - Paul Barry (pbarry(AT)wit.ie), Jan 25 2004
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EXAMPLE
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1; 0,1; -1,0,1; -2,-3,0,1; -3,-8,-6,0,1; ...
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PROGRAM
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(PARI) T(n, k)=(1-n+k)*if(k<0|k>n, 0, n!/k!/(n-k)!)
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CROSSREFS
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Absolute values of columns 1, 2: A005563, A005564.
Sequence in context: A112168 A072516 A106450 this_sequence A128888 A004443 A008290
Adjacent sequences: A055134 A055135 A055136 this_sequence A055138 A055139 A055140
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KEYWORD
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sign,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Apr 25 2000
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EXTENSIONS
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Additional comments from Michael Somos, Jul 04 2002
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