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Partial sums of sequence {1/(i^2+1): i=0..n} (denominators).
3

%I #12 Apr 27 2020 17:34:42

%S 1,2,10,5,85,2210,81770,204425,204425,16762850,1693047850,51637959425,

%T 1497500823325,2995001646650,590015324390050,33335865828037825,

%U 8567317517805721025,17134635035611442050

%N Partial sums of sequence {1/(i^2+1): i=0..n} (denominators).

%H Robert Israel, <a href="/A033468/b033468.txt">Table of n, a(n) for n = 0..389</a>

%p S:= 0:

%p for i from 0 to 50 do

%p S:= S + 1/(i^2+1);

%p A[i]:= denom(S)

%p od:

%p seq(A[i],i=0..50); # _Robert Israel_, Apr 27 2020

%t Accumulate[Table[1/(n^2+1),{n,0,20}]]//Denominator (* _Harvey P. Dale_, Jan 20 2020 *)

%o (PARI) for(n=0,20,print1(denominator(sum(k=0,n,1/(k^2+1))),", ")) \\ _Hugo Pfoertner_, Apr 27 2020

%Y Cf. A033467.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.