%I A053557
%S A053557 1,0,1,1,3,11,53,103,2119,16687,16481,1468457,16019531,63633137,2467007773,
%T A053557 34361893981,15549624751,8178130767479,138547156531409,92079694567171,
%U A053557 4282366656425369,72289643288657479,6563440628747948887,39299278806015611311
%N A053557 Numerator of Sum_{k=0..n} (-1)^k/k!.
%C A053557 Numerator of probability of a derangement of n things (A000166(n)/n! 
               or !n/n!).
%C A053557 Also denominators 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+...))))))).
%D A053557 L. Lorentzen and H. Waadeland, Continued Fractions with Applications, 
               North-Holland 1992, p. 562.
%D A053557 E. Maor, e: The Story of a Number, Princeton Univ. Press 1994, pp. 151 
               and 157.
%H A053557 T. D. Noe, <a href="b053557.txt">Table of n, a(n) for n=0..100</a>
%H A053557 Leonhardo Eulero, <a href="http://gallica.bnf.fr/scripts/ConsultationTout.exe?E=0&O=N003351">
               Introductio in analysin infinitorum. Tomus primus</a>, Lausanne, 
               1748.
%H A053557 L. Euler, Introduction a l'analyse infinitesimal <a href="http://gallica.bnf.fr/
               scripts/ConsultationTout.exe?E=0&O=N003884">Tome premier</a>, <a 
               href="http://gallica.bnf.fr/scripts/ConsultationTout.exe?E=0&O=N003885">
               Tome second</a>, trad. du latin en francais par J. B. Labey, Paris, 
               1796-1797.
%H A053557 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Subfactorial.html">Subfactorial</a> [From Eric W. Weisstein (eric(AT)weisstein.com), 
               Sep 12 2008]
%H A053557 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ContinuedFractionConstant.html">Continued Fraction Constant</a> [From 
               Eric W. Weisstein (eric(AT)weisstein.com), Oct 03 2008]
%F A053557 Let -e^(-x)/(x-1)= Sum(n, 0, infty)a_n/b_n *x^n . Then sequence a_n is 
               A053557 - Aleksandar Petojevic (apetoje(AT)ptt.yu), Apr 14 2004
%e A053557 1, 0, 1/2, 1/3, 3/8, 11/30, 53/144, 103/280, 2119/5760, ...
%Y A053557 Cf. A000166/A000142, A053556 (denominators), A053518-A053520. See also 
               A103816.
%Y A053557 a(n) = (N(n, n) of A103361), A053557/A053556 = A000166/n! = (N(n, n) 
               of A103361)/(D(n, n) of A103360), Cf. A053518-A053520.
%Y A053557 Sequence in context: A054362 A129833 A107958 this_sequence A039302 A074512 
               A005502
%Y A053557 Adjacent sequences: A053554 A053555 A053556 this_sequence A053558 A053559 
               A053560
%K A053557 nonn,frac,nice,easy
%O A053557 0,5
%A A053557 N. J. A. Sloane (njas(AT)research.att.com), Jan 17 2000
%E A053557 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 31 2000