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%I #17 Aug 04 2014 20:44:07
%S 1,4,9,40,195,1176,8225,65808,592263,5922640,65149029,781788360,
%T 10163248667,142285481352,2134282220265,34148515524256,
%U 580524763912335,10449445750422048,198539469258018893,3970789385160377880,83386577088367935459,1834504695944094580120
%N a(1)=1, then add 1 multiply by 2 to get a(2), subtract 1 and multiply by 3 to get a(3), add 1 and multiply by 4 to get a(4) and so on.
%H Robert Israel, <a href="/A085110/b085110.txt">Table of n, a(n) for n = 1..372</a>
%F a(1)=1, a(n)=n*a(n-1)+(-1)^n*n ; a(n)=round(n!*(2-exp(-1)))+(-1)^n. - _Benoit Cloitre_, Sep 24 2006
%F E.g.f.: t*(exp(-t)-2)/(t-1). - _Robert Israel_, Aug 04 2014
%F a(n) = ((n-2)*n/(n-1))*a(n-1) + n*a(n-2). - _Robert Israel_, Aug 04 2014
%p a[1]:= 1:
%p for n from 2 to 30 do a[n]:= n*(a[n-1]+(-1)^n) od:
%p seq(a(n), n=1..30); # _Robert Israel_, Aug 04 2014
%t nxt[{n_,a_}]:={n+1,If[OddQ[n],(n+1)(a+1),(n+1)(a-1)]}; Transpose[ NestList[ nxt,{1,1},30]][[2]] (* _Harvey P. Dale_, Aug 04 2014 *)
%o (PARI) a(n)=if(n<2,1,n*a(n-1)+(-1)^n*n) \\ _Benoit Cloitre_, Sep 24 2006
%K nonn
%O 1,2
%A _Amarnath Murthy_, Jul 04 2003
%E More terms from _Sam Alexander_, Feb 26 2004
%E Corrected and extended by _Harvey P. Dale_, Aug 04 2014
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