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Search: id:A006154
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| A006154 |
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Number of labeled ordered partitions of an n-set into odd parts.
(Formerly M1792)
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+0
8
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| 1, 1, 2, 7, 32, 181, 1232, 9787, 88832, 907081, 10291712, 128445967, 1748805632, 25794366781, 409725396992, 6973071372547, 126585529106432, 2441591202059281, 49863806091395072, 1074927056650469527
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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With alternating signs, e.g.f.: 1/(1+sinh(x)). - R. Stephan, Apr 29 2004
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REFERENCES
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Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. Ars Combin. 10 (1980), 131-145.
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FORMULA
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E.g.f.: 1/(1 - sinh x).
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
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)].
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PROGRAM
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(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)
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CROSSREFS
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Cf. A000045, A000670.
Sequence in context: A121555 A097900 A000153 this_sequence A000987 A006957 A079265
Adjacent sequences: A006151 A006152 A006153 this_sequence A006155 A006156 A006157
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Simon Plouffe (plouffe(AT)math.uqam.ca)
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EXTENSIONS
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More terms from Christian G. Bower (bowerc(AT)usa.net), Oct 15 1999.
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