A131445 Numerators of n-th approximation of factorial (also called harmonic) expansion of Pi.

3, 3, 3, 25, 47, 2261, 15833, 42223, 42223, 11400211, 1672031, 136802537, 2173640311, 2173640311, 342348348983, 5975534818613, 372475003693547, 21511925347007, 76431870757915873, 56199904969055789, 4223866541884824563

Offset

1,1

Comments

Denominators are given in A131446. Rationals in lowest terms.

Links

Table of n, a(n) for n=1..21.

W. Lang, Rationals and values.

Formula

a(n) = numerator(r(n)), with r(n) = Sum_{k=1..n} b(k)/k! with b(k) = A075874(k) (factorial expansion of Pi).

Example

Rationals r(n): 3, 3, 3, 25/8, 47/15, 2261/720, 15833/5040, 42223/13440, 42223/13440, ...

Crossrefs

Sequence in context: A127014 A073748 A289118 * A230176 A033874 A122092

Adjacent sequences: A131442 A131443 A131444 * A131446 A131447 A131448

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Aug 07 2007

Status

approved