Search: id:A006154
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%I A006154 M1792
%S A006154 1,1,2,7,32,181,1232,9787,88832,907081,10291712,128445967,1748805632,
%T A006154 25794366781,409725396992,6973071372547,126585529106432,
%U A006154 2441591202059281,49863806091395072,1074927056650469527
%N A006154 Number of labeled ordered partitions of an n-set into odd parts.
%C A006154 With alternating signs, e.g.f.: 1/(1+sinh(x)). - R. Stephan, Apr 29 2004
%D A006154 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006154 Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. 
               Ars Combin. 10 (1980), 131-145.
%F A006154 E.g.f.: 1/(1 - sinh x).
%F A006154 a(0)=a(1)=1, a(n) = sum[k=1..ceil(n/2), C(n, 2k-1) * a(n-2k+1)]. - R. 
               Stephan, Apr 29 2004
%F A006154 a(n) ~ (sqrt(2)/2)*n!/log(1+sqrt(2))^(n+1). - Conjectured by Simon Plouffe, 
               Feb 17 2007. Comment from A. N. W. Hone (A.N.W.Hone(AT)kent.ac.uk), 
               Feb 22 2007: This formula can be proved using the techniques in the 
               article by Philippe Flajolet, Symbolic Enumerative Combinatorics 
               and Complex Asymptotic Analysis, Algorithms Seminar 2000-2001, F. 
               Chyzak (ed.), INRIA, (2002), pp. 161-170 [see Theorem 5 and Table 
               2, noting that 1/(1-sinh(x)) just has a simple pole at x=log(1+sqrt(2)].
%o A006154 (PARI) a(n)=if(n<2,n>=0,sum(k=1,ceil(n/2),binomial(n,2*k-1)*a(n-2*k+1))) 
               (from R. Stephan)
%Y A006154 Cf. A000045, A000670.
%Y A006154 Sequence in context: A121555 A097900 A000153 this_sequence A000987 A006957 
               A079265
%Y A006154 Adjacent sequences: A006151 A006152 A006153 this_sequence A006155 A006156 
               A006157
%K A006154 nonn,easy,nice
%O A006154 0,3
%A A006154 Simon Plouffe (simon.plouffe(AT)gmail.com)
%E A006154 More terms from Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.

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