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%I M3652 N1485 #19 Nov 25 2015 01:53:08
%S 1,1,4,33,480,11010,367560,16854390,1016930880,78124095000,
%T 7446314383200,862332613342200,119261328828364800,
%U 19415283189746043600,3675162134109650184000,800409618620667941886000,198730589981586780813696000,55800304882692417053710704000
%N From a distribution problem.
%D H. Anand, V. C. Dumir and H. Gupta, A combinatorial distribution problem, Duke Math. J., 33 (1996), 757-769.
%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).
%F a(n) = n*(2*n-1)*b(n) - n*(n-1)^2*b(n-1), b(n) = A000681(n).
%t b[n_] := Sum[(2i)!*n!^2/(2^i*i!^2*(n-i)!), {i, 0, n}]/2^n; a[n_] := n*(2n-1)*b[n-1] - n*(n-1)^2*b[n-2]; a[0]=1; Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Aug 08 2012, after formula *)
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_
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