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 A002020 a(n+1) = a(n) - n*(n-1)*a(n-1), with a(n) = 1 for n <= 3. (Formerly M3876 N1588) 5

%I M3876 N1588

%S 1,1,1,1,-5,-17,83,593,-2893,-36101,172195,3421285,-15520165,

%T -467129785,1954015955,86971636825,-323371713725,-21196564551725,

%U 66760541581475,6552909294409325,-16279195926455125,-2506384727801998625,4330877561309153875

%N a(n+1) = a(n) - n*(n-1)*a(n-1), with a(n) = 1 for n <= 3.

%D R. Kelisky, The numbers generated by exp(arctan x), Duke Math. J., 26 (1959), 569-581.

%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).

%H T. D. Noe, <a href="/A002020/b002020.txt">Table of n, a(n) for n = 0..100</a>

%p f := proc(n) option remember; if n<=3 then 1 else f(n-1)-(n-1)*(n-2)*f(n-2); fi; end;

%t t = {1, 1, 1, 1}; Do[AppendTo[t, t[[-1]] - (n-1) (n - 2) t[[-2]]], {n, 4, 20}] (* _T. D. Noe_, Aug 30 2012 *)

%K sign,easy

%O 0,5

%A _N. J. A. Sloane_.

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