|
| |
|
|
A058087
|
|
Triangle giving coefficients of menage hit polynomials.
|
|
10
| |
|
|
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; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| 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.
|
|
|
FORMULA
| G.f.: x*y+(1-x*(y-1))*Sum(n!*(x*y)^n/(1+x*(y-1))^(2*n+1),n=0..infinity). [From Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 14 2009]
|
|
|
EXAMPLE
| 1; 2,0; 2,0,0; 2,3,0,1; 2,8,4,8,2; ...
|
|
|
MAPLE
| 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.
|
|
|
CROSSREFS
| Diagonals give A000179, A000425, A000033, A000159, A000181, A000185, A058089, A058090.
Essentially a mirror image of A094314.
Sequence in context: A035220 A128765 A193511 * A073274 A192323 A071957
Adjacent sequences: A058084 A058085 A058086 * A058088 A058089 A058090
|
|
|
KEYWORD
| nonn,easy,tabl,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 02 2000
|
| |
|
|
