Search: id:A005649
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%I A005649 M1866
%S A005649 1,2,8,44,308,2612,25988,296564,3816548,54667412,862440068,14857100084,
%T A005649 277474957988,5584100659412,120462266974148,2772968936479604,67843210855558628,
%U A005649 1757952715142990612,48093560991292628228,1385244691781856307124
%N A005649 Expansion of (2 - e^x)^(-2).
%C A005649 Exponential self-convolution of numbers of preferential arrangements.
%C A005649 Number of compatible bipartitional relations on a set of cardinality 
               n. - Ralf Stephan, Apr 27 2003
%C A005649 Stirling transform of A052558 : 1, 1, 4, 12, 72, 360, . . . - Philippe 
               DELEHAM, May 17 2005
%C A005649 With an extra 1 at the beginning, coefficients of the formal (divergent) 
               series expansion at infinity of Sum_{k>=0} 1/binomial(x,k) = 1+1/
               x+2/x^2+8/x^3+... Also Sum_{k>=0} k!/x^k Product_{i=1..k-1} 1/(1- 
               i/x) yields a generating function in 1/x - Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), 
               Nov 21 2000
%D A005649 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005649 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.
%H A005649 T. D. Noe, <a href="b005649.txt">Table of n, a(n) for n=0..100</a>
%H A005649 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=154">
               Encyclopedia of Combinatorial Structures 154</a>
%H A005649 Foata, D. and Krattenthaler, C., <a href="http://citeseer.ist.psu.edu/
               foata95graphical.html">Graphical Major Indices, II</a>, Seminaire 
               Lotharingien de Combinatoire, B34k, 16 pp., 1995.
%H A005649 D. Foata and D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9406220">
               [math/9406220] The Graphical Major Index</a>
%F A005649 E.g.f.: 1/(2-exp(x))^2.
%F A005649 a(n) = (A000670(n) + A000670(n+1)) / 2 . - Philippe DELEHAM, May 16 2005
%t A005649 Sum[(i + j)^n/2^(2 + i + j), {i, 0, Infinity}, {j, 0, Infinity}] [From 
               Vladimir Reshetnikov (v.reshetnikov(AT)gmail.com), Dec 31 2008]
%o A005649 (PARI) a(n)=if(n<0,0,n!*polcoeff(subst(1/(1-y)^2,y,exp(x+x*O(x^n))-1),
               n))
%Y A005649 Cf. A000670.
%Y A005649 2*A083410(n)=a(n), if n>0.
%Y A005649 Pairwise sums of A052841 and also of A089677.
%Y A005649 Sequence in context: A075792 A052897 A137984 this_sequence A005363 A123307 
               A126101
%Y A005649 Adjacent sequences: A005646 A005647 A005648 this_sequence A005650 A005651 
               A005652
%K A005649 nonn,easy,nice
%O A005649 0,2
%A A005649 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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