0,3

Denominator of probability of a derangement of n things (A000166(n)/n!).

Also numerators of successive convergents to e using continued fraction 2+1/(1+1/(2+2/(3+3/(4+4/(5+5/(6+6/(7+7/8+...))))))).

L. Lorentzen and H. Waadeland, Continued Fractions with Applications, North-Holland 1992, p. 562.

E. Maor, e: The Story of a Number, Princeton Univ. Press 1994, pp. 151 and 157.

T. D. Noe, Table of n, a(n) for n=0..100

Leonhardo Eulero, Introductio in analysin infinitorum. Tomus primus, Lausanne, 1748.

L. Euler, Introduction a l'analyse infinitesimal Tome premier, Tome second, trad. du latin en francais par J. B. Labey, Paris, 1796-1797.

%H A053556 Eric Weisstein's World of Mathematics, Subfactorial [From Eric W. Weisstein (eric(AT)weisstein.com), Sep 12 2008]

Let -e^(-x)/(x-1)= Sum(n, 0, infty)a_n/b_n *x^n . Then sequence b_n is A053556 - Aleksandar Petojevic (apetoje(AT)ptt.yu), Apr 14 2004

1, 0, 1/2, 1/3, 3/8, 11/30, 53/144, 103/280, 2119/5760, ...

Table[ Denominator[ Sum[ -(-1)^k/k!, {k, 0, n}]], {n, 0, 20}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 13 2005)

Cf. A053557 (numerators), A053518-A053520. See also A103816.

a(n) = (D(n, n) of A103360), A053557/A053556 = A000166/n! = (N(n, n) of A103361)/(D(n, n) of A103360), Cf. A053518-A053520.

Adjacent sequences: A053553 A053554 A053555 this_sequence A053557 A053558 A053559

Sequence in context: A012886 A078918 A054104 this_sequence A001048 A141520 A072042

nonn,frac,nice,easy

N. J. A. Sloane (njas(AT)research.att.com), Jan 17 2000

More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 31 2000