Search: id:A058087
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%I A058087
%S A058087 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,
%T A058087 80,2,35,140,469,994,1477,1344,579,2,48,280,1232,3660,7888,11672,
%U A058087 10800,4738,2,63,504,2856,11268,32958,70152,104256,97434,43387
%N A058087 Triangle giving coefficients of menage hit polynomials.
%D A058087 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               198.
%D A058087 Anthony C. Robin, Circular Wife Swapping, The Mathematical Gazette, November 
               2006.
%D A058087 I. Kaplansky and J. Riordan. The probleme des menages. Scripta Mathematica 
               1946, 12 (2), 113-124.
%F A058087 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]
%e A058087 1; 2,0; 2,0,0; 2,3,0,1; 2,8,4,8,2; ...
%p A058087 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.
%Y A058087 Diagonals give A000179, A000425, A000033, A000159, A000181, A000185, 
               A058089, A058090.
%Y A058087 Essentially a mirror image of A094314.
%Y A058087 Sequence in context: A091395 A035220 A128765 this_sequence A073274 A071957 
               A002655
%Y A058087 Adjacent sequences: A058084 A058085 A058086 this_sequence A058088 A058089 
               A058090
%K A058087 nonn,easy,tabl,nice,new
%O A058087 0,2
%A A058087 N. J. A. Sloane (njas(AT)research.att.com), Dec 02 2000

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