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a(1) = 1; a(n) = -Sum_{k = 1..n-1} (n+k)!a(k)/(2k)!.
(Formerly M2289)
2

%I M2289 #14 Jan 10 2018 03:12:00

%S 1,-3,3,9,21,-33,-1173,-13515,-113739,-532209,6284379,264830061,

%T 5897799141,104393462439,1459983940203,10308316834293,

%U -308010522508395,-19576840707893409,-726806556195360069,-22261372611370303875,-591210850189999983099

%N a(1) = 1; a(n) = -Sum_{k = 1..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)

%Y Cf. A067000.

%K sign

%O 1,2

%A _N. J. A. Sloane_