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Search: id:A058057
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| A058057 |
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Triangle giving coefficients of menage hit polynomials. |
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+0
8
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| 1, 1, 0, 1, 1, 0, 1, 3, 1, 1, 1, 6, 6, 8, 3, 1, 10, 20, 38, 35, 16, 1, 15, 50, 134, 213, 211, 96, 1, 21, 105, 385, 915, 1479, 1459, 675, 1, 28, 196, 952, 3130, 7324, 11692, 11584, 5413, 1, 36, 336, 2100, 9090, 28764, 65784, 104364, 103605, 48800
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Triangle of coefficients of polynomials P(n; x) = Permanent(M), where M=[m(i,j)] is n X n matrix defined by m(i,j)=x if 0<=i-j<=1 else m(i,j)=1. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 23 2003
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.
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EXAMPLE
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1; 1,0; 1,1,0; 1,3,1,1; 1,6,6,8,3; ...
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MAPLE
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V := proc(n) local k; add( binomial(2*n-k, k)*(n-k)!*(x-1)^k, k=0..n); end; W := proc(r, s) coeff( V(r), x, s ); end; a := (n, k)->W(n, n-k);
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CROSSREFS
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Diagonals give A000271, A000426, A000222, A000386, A000450, A058085, A058086.
Cf. A080018, A080061.
Sequence in context: A016566 A096744 A080002 this_sequence A124372 A126470 A102480
Adjacent sequences: A058054 A058055 A058056 this_sequence A058058 A058059 A058060
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KEYWORD
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nonn,easy,nice,tabl
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AUTHOR
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njas, Dec 02 2000
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