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A144656 a(n) = (n mod 2) if n <= 3, otherwise a(n) = (n^2-5n+7)*(n-2)*a(n-1)/(n-3) + (n^2-5n+7)*a(n-2) - (n-2)*a(n-3)/(n-3). 1

%I

%S 0,1,0,1,4,49,900,24649,944784,48455521,3210355600,267186643801,

%T 27307626948900,3363915436531441,491705171699154084,

%U 84158959760104032049,16675767262618669710400,3787671541267275818341249,977702867682508392324162624,284628954669920840314598014801

%N a(n) = (n mod 2) if n <= 3, otherwise a(n) = (n^2-5n+7)*(n-2)*a(n-1)/(n-3) + (n^2-5n+7)*a(n-2) - (n-2)*a(n-3)/(n-3).

%C Terms are squares; square roots give A001053.

%D M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 35.

%H S. B. Ekhad, <a href="http://www.jstor.org/stable/2325130">Problem 10356</a>, Amer. Math. Monthly, 101 (1994), 75.

%p a:=proc(n) option remember; local m;

%p if n=0 then RETURN(0); fi;

%p if n=1 then RETURN(1); fi;

%p if n=2 then RETURN(0); fi;

%p if n=3 then RETURN(1); fi;

%p m:=n-3;

%p RETURN((m^2+m+1)*(m+1)*a(n-1)/m+(m^2+m+1)*a(n-2)-(m+1)*a(n-3)/m);

%p end;

%o (PARI) a=vector(10^3); for(n=1, 3, a[n]=n%2); for(n=4, #a, a[n] = (n^2-5*n+7)*(n-2)*a[n-1]/(n-3) + (n^2-5*n+7)*a[n-2] - (n-2)*a[n-3]/(n-3)); concat(0, a) \\ _Altug Alkan_, Apr 04 2018

%Y Cf. A001053.

%K nonn

%O 0,5

%A _N. J. A. Sloane_, Jan 30 2009

%E Typo in name corrected by _Rogério Serôdio_, Apr 04 2018

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Last modified March 31 16:02 EDT 2020. Contains 333151 sequences. (Running on oeis4.)