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%I M5044 #18 Jan 10 2018 03:11:52
%S 1,-1,1,1,-1,-17,-107,-415,1231,56671,924365,11322001,97495687,
%T -78466897,-31987213451,-1073614991039,-26754505127713,
%U -558657850929473,-9259584394031075,-70982644052430799,3334438016903221111,240585292388924690959,10679411902033402697861
%N a(n) = -Sum_{k = 0..n-1} (n+k)!a(k)/(2k)!.
%D H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H H. W. Gould, <a href="/A007680/a007680.pdf">A class of binomial sums and a series transform</a>, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy)
%p A007682 := proc(n) option remember; if n=0 then RETURN(1) fi; if n>0 then RETURN((-1)*add((n+k)!*'A007682(k)'/(2*k)!, k=0..n-1 )) fi; end;
%t a[n_] := a[n] = -Sum[(n+k)!*a[k]/(2*k)!, {k, 0, n-1}]; a[0] = 1; Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Jan 27 2014 *)
%K sign,easy,nice
%O 0,6
%A _N. J. A. Sloane_
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