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

Author

Wolfdieter Lang, Aug 07 2007

Keywords

• nonn
• frac
• easy

Comments

Denominators are given in A131446. Rationals in lowest terms.

Examples

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

Links

• 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).