%I A010842
%S A010842 1,3,10,38,168,872,5296,37200,297856,2681216,26813184,294947072,
%T A010842 3539368960,46011804672,644165281792,9662479259648,154599668219904,
%U A010842 2628194359869440,47307498477912064,898842471080853504
%N A010842 E.g.f.: exp(2x)/(1-x).
%C A010842 Incomplete Gamma Function at 2.
%C A010842 Let P(A) be the power set of an n-element set A. Then a(n) = the total 
               number of ways to add 0 or more elements of A to each element x of 
               P(A) where the elements to add are not elements of x and order of 
               addition is important. - Ross La Haye (rlahaye(AT)new.rr.com), Nov 
               19 2007
%D A010842 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 262.
%D A010842 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see 
               Example 5.1.2.
%D A010842 Ross La Haye, Binary Relations on the Power Set of an n-Element Set, 
               Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6. [From 
               Ross La Haye (rlahaye(AT)new.rr.com), Feb 22 2009]
%H A010842 T. D. Noe, <a href="b010842.txt">Table of n, a(n) for n=0..100</a>
%H A010842 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A010842 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 262.
%H A010842 J. W. Layman, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               The Hankel Transform and Some of its Properties</a>, J. Integer Sequences, 
               4 (2001), #01.1.5.
%F A010842 a(n) = row sums of A090802. - Ross La Haye (rlahaye(AT)new.rr.com), Aug 
               18 2006
%F A010842 a(n) = n*a(n-1)+2^n = (n+2)a(n-1)-(2n-2)a(n-2) = n!*sum{0 <= j <= n}[ 
               2^j/j! ] - Henry Bottomley (se16(AT)btinternet.com), Jul 12 2001
%F A010842 a(n) is the permanent of the n X n matrix with 3's on the diagonal and 
               1's elsewhere. a(n) = Sum(k=0..n, A008290(n, k)*3^k). - DELEHAM Philippe 
               (kolotoko(AT)wanadoo.fr), Dec 12 2003
%F A010842 Binomial transform of A000522. - Ross La Haye (rlahaye(AT)new.rr.com), 
               Sep 15 2004
%F A010842 a(n)=sum{k=0..n, k!*C(n, k)2^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), 
               Apr 22 2005
%F A010842 a(n) = A066534(n) + 2^n. - Ross La Haye (rlahaye(AT)new.rr.com), Nov 
               16 2005
%F A010842 a(n) is the number of ways to split the set {1,2,...,n} into two disjoint 
               subsets S,T with S union T = {1,2,...,n} and linearly order S and 
               then choose a subset of T. [From Geoffrey Critzer (critzer.geoffrey(AT)usd443.org), 
               Mar 10 2009]
%p A010842 restart: G(x):=exp(2*x)/(1-x): f[0]:=G(x): for n from 1 to 19 do f[n]:=diff(f[n-1],
               x) od: x:=0: seq(f[n],n=0..19);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 03 2009]
%t A010842 Table[ Gamma[ n, 2 ]*E^2, {n, 1, 24} ]
%Y A010842 Cf. A053484, A053485, A053486, A008290.
%Y A010842 A010843, A000023, A000166, A000142, A000522, A010842, A053486, A053487 
               have similar properties.
%Y A010842 Sequence in context: A151063 A103138 A074527 this_sequence A140710 A103296 
               A111749
%Y A010842 Adjacent sequences: A010839 A010840 A010841 this_sequence A010843 A010844 
               A010845
%K A010842 nonn,nice,easy
%O A010842 0,2
%A A010842 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)