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%I #10 Apr 28 2020 00:16:46
%S 1,3,17,9,158,4193,157351,397466,400611,33054527,3355270077,
%T 102758999311,2990338571904,5998294800553,1184659077355591,
%U 67080741701688404,17273086483161957653,34605257914722575451,6931595973735660593,628166167374857855769,252204770011462567264474
%N Partial sums of sequence {1/(i^2+1): i=0..n} (numerators).
%e Take the sequence
%e 1, 1/2, 1/5, 1/10, 1/17, 1/26, 1/37, 1/50, 1/65, 1/82, 1/101, 1/122, 1/145, 1/170, 1/197, 1/226, ...,
%e take partial sums:
%e 1, 3/2, 17/10, 9/5, 158/85, 4193/2210, 157351/81770, 397466/204425, 400611/204425, 33054527/16762850, 3355270077/1693047850, ...,
%e take numerators:
%e 1, 3, 17, 9, 158, 4193, 157351, 397466, 400611, 33054527, 3355270077, 102758999311, ...
%t Accumulate[Table[1/(n^2+1),{n,0,20}]]//Numerator (* _Harvey P. Dale_, Jan 20 2020 *)
%o (PARI) for(n=0,20,print1(numerator(sum(k=0,n,1/(k^2+1))),", ")) \\ _Hugo Pfoertner_, Apr 27 2020
%Y Denominators are in A033468.
%K nonn
%O 0,2
%A _N. J. A. Sloane_.
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