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Search: id:A058087
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| A058087 |
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Triangle giving coefficients of menage hit polynomials. |
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11
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| 1, 2, 0, 2, 0, 0, 2, 3, 0, 1, 2, 8, 4, 8, 2, 2, 15, 20, 40, 30, 13, 2, 24, 60, 152, 210, 192, 80, 2, 35, 140, 469, 994, 1477, 1344, 579, 2, 48, 280, 1232, 3660, 7888, 11672, 10800, 4738, 2, 63, 504, 2856, 11268, 32958, 70152, 104256, 97434, 43387
(list; table; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.
Anthony C. Robin, Circular Wife Swapping, The Mathematical Gazette, November 2006.
I. Kaplansky and J. Riordan. The probleme des menages. Scripta Mathematica 1946, 12 (2), 113-124.
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EXAMPLE
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1; 2,0; 2,0,0; 2,3,0,1; 2,8,4,8,2; ...
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MAPLE
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U := proc(n) local k; add( (2*n/(2*n-k))*binomial(2*n-k, k)*(n-k)!*(x-1)^k, k=0..n); end; W := proc(r, s) coeff( U(r), x, s ); end; a := (n, k)->W(n, n-k); # valid for n >= 2.
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CROSSREFS
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Diagonals give A000179, A000425, A000033, A000159, A000181, A000185, A058089, A058090.
Essentially a mirror image of A094314.
Sequence in context: A091395 A035220 A128765 this_sequence A073274 A071957 A002655
Adjacent sequences: A058084 A058085 A058086 this_sequence A058088 A058089 A058090
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KEYWORD
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nonn,easy,tabl,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 02 2000
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