A095823 Denominators of certain upper bounds for Euler's number e.

1, 4, 18, 32, 600, 4320, 11760, 322560, 3265920, 1728000, 439084800, 821145600, 817689600, 1220496076800, 19615115520000, 111588212736000, 863812325376000, 115242726703104000, 15722836107264000, 3742926166425600000

Offset

1,2

Comments

For the numerators see A095822.

e := Sum_{k>=0} 1/k! has (trivial) upper bound r(n) := A095822(n)/a(n), for every n >= 1. See the W. Lang link.

References

M. Barner and F. Flohr, Analysis I, de Gruyter, 5te Auflage, 2000; pp. 117/8.

E. Kuz'min and A. I. Shirshov: On the number e, pp. 111-119, eq.(6), in: Kvant Selecta: Algebra and Analysis, I, ed. S. Tabachnikov, Am.Math.Soc., 1999

Links

Table of n, a(n) for n=1..20.

W. Lang, r(n) numbers and comments.

Formula

a(n) = denominator(r(n)), with rational r(n) := (Sum_{k=0..n} 1/k!) + 1/(n*n!), n >= 1, written in lowest terms. For n*n! see A001563(n).

Example

The positive rationals r(n), n >= 1: 3/1, 11/4, 49/18, 87/32, 1631/600, 11743/4320, 31967/11760, ...

Crossrefs

Sequence in context: A053191 A003474 A337003 * A092116 A083969 A110621

Adjacent sequences: A095820 A095821 A095822 * A095824 A095825 A095826

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jun 11 2004

Status

approved