A131447 Numerators of n-th approximation of factorial (also called harmonic) expansion of Euler's constant gamma (A001620).

0, 1, 1, 13, 23, 83, 2909, 23273, 3491, 3491, 11520301, 30720803, 30720803, 50320675319, 68619102709, 3019240519199, 4666098984217, 1847775197749939, 23405152504832563, 1404309150289953793, 9830164052029676557

Offset: 1

Author

Wolfdieter Lang, Aug 07 2007

Keywords

• nonn
• frac
• easy

Comments

Rationals are in lowest terms.

Examples

			Rationals r(n): [0, 1/2, 1/2, 13/24, 23/40, 83/144, 2909/5040, 23273/40320, 3491/6048, ...]
		

References

• J. Havil, Gamma, (in German), Springer, 2007, p. 118; Gamma: Exploring Euler's Constant, Princeton Univ. Press, 2003.

Links

• Wolfdieter Lang, Rationals and values.

Crossrefs

Cf. A001620, A096622, A131448 (denominators)

Formula

a(n) = numerator(r(n)), with r(n) = Sum_{k=1..n} b(k)/k!, and b(k) = A096622(k) (factorial expansion of gamma).