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A033467

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

1, 3, 17, 9, 158, 4193, 157351, 397466, 400611, 33054527, 3355270077, 102758999311, 2990338571904, 5998294800553, 1184659077355591, 67080741701688404, 17273086483161957653, 34605257914722575451, 6931595973735660593, 628166167374857855769, 252204770011462567264474 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	LINKS	`Table of n, a(n) for n=0..20.`
	EXAMPLE	`Take the sequence` `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, ...,` `take partial sums:` `1, 3/2, 17/10, 9/5, 158/85, 4193/2210, 157351/81770, 397466/204425, 400611/204425, 33054527/16762850, 3355270077/1693047850, ...,` `take numerators:` `1, 3, 17, 9, 158, 4193, 157351, 397466, 400611, 33054527, 3355270077, 102758999311, ...`
	MATHEMATICA	`Accumulate[Table[1/(n^2+1), {n, 0, 20}]]//Numerator (* Harvey P. Dale, Jan 20 2020 *)`
	PROG	`(PARI) for(n=0, 20, print1(numerator(sum(k=0, n, 1/(k^2+1))), ", ")) \\ Hugo Pfoertner, Apr 27 2020`
	CROSSREFS	`Denominators are in A033468.` `Sequence in context: A273249 A273303 A362086 * A096475 A088122 A357373` `Adjacent sequences: A033464 A033465 A033466 * A033468 A033469 A033470`
	KEYWORD	`nonn`
	AUTHOR	`N. J. A. Sloane.`
	STATUS	`approved`

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)