Search: id:A053556
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%I A053556
%S A053556 1,1,2,3,8,30,144,280,5760,45360,44800,3991680,43545600,172972800,
%T A053556 6706022400,93405312000,42268262400,22230464256000,376610217984000,
%U A053556 250298560512000,11640679464960000,196503623737344000,17841281393295360000
%N A053556 Denominator of Sum_{k=0..n} (-1)^k/k!.
%C A053556 Denominator of probability of a derangement of n things (A000166(n)/n!).
%C A053556 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+...))))))).
%D A053556 L. Lorentzen and H. Waadeland, Continued Fractions with Applications, 
               North-Holland 1992, p. 562.
%D A053556 E. Maor, e: The Story of a Number, Princeton Univ. Press 1994, pp. 151 
               and 157.
%H A053556 T. D. Noe, <a href="b053556.txt">Table of n, a(n) for n=0..100</a>
%H A053556 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 A053556 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 A053556 %H A053556 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]
%F A053556 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
%e A053556 1, 0, 1/2, 1/3, 3/8, 11/30, 53/144, 103/280, 2119/5760, ...
%t A053556 Table[ Denominator[ Sum[ -(-1)^k/k!, {k, 0, n}]], {n, 0, 20}] (from Robert 
               G. Wilson v (rgwv(at)rgwv.com), Oct 13 2005)
%Y A053556 Cf. A053557 (numerators), A053518-A053520. See also A103816.
%Y A053556 a(n) = (D(n, n) of A103360), A053557/A053556 = A000166/n! = (N(n, n) 
               of A103361)/(D(n, n) of A103360), Cf. A053518-A053520.
%Y A053556 Sequence in context: A012886 A078918 A054104 this_sequence A001048 A141520 
               A072042
%Y A053556 Adjacent sequences: A053553 A053554 A053555 this_sequence A053557 A053558 
               A053559
%K A053556 nonn,frac,nice,easy
%O A053556 0,3
%A A053556 N. J. A. Sloane (njas(AT)research.att.com), Jan 17 2000
%E A053556 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 31 2000

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