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%I M4137 N1715 #21 Feb 01 2022 00:55:27
%S 0,0,0,1,6,20,134,915,7324,65784,657180,7223637,86637650,1125842556,
%T 15757002706,236298742375,3780061394232,64251145312880,
%U 1156374220457784,21968796934412649,439337048505773790,9225384943965382564,202945418255342821470
%N Coefficients of ménage hit polynomials.
%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%t max = 22; f[x_, y_] := Sum[n!*((x*y)^n/(1+x*(y-1))^(2*n+1)), {n, 0, max}]; t = MapIndexed[Take[#1, #2[[1]]]&, CoefficientList[Series[f[x, y], {x, 0, max}, {y, 0, max}], {x, y}]]; a[n_] := If[n<3, 0, t[[n+1, n-2]]]; Table[ a[n], {n, 0, max}] (* _Jean-François Alcover_, Feb 08 2016, after _Vladeta Jovovic_ in A058057 *)
%Y A diagonal of A058057.
%K nonn
%O 0,5
%A _N. J. A. Sloane_
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