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

1,4

Comments

Rationals are in lowest terms.

References

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

Links

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

Wolfdieter Lang, Rationals and values.

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).

Example

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

Crossrefs

Cf. A001620, A096622, A131448 (denominators)

Sequence in context: A046862 A155093 A147443 * A110196 A039448 A299361

Adjacent sequences: A131444 A131445 A131446 * A131448 A131449 A131450

Keyword

nonn,frac,easy,changed

Author

Wolfdieter Lang, Aug 07 2007

Status

approved