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Search: id:A006153
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| A006153 |
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Expansion of 1/(1-x*exp(x)).
(Formerly M3578)
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+0
2
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| 1, 1, 4, 21, 148, 1305, 13806, 170401, 2403640, 38143377, 672552730, 13044463641, 276003553860, 6326524990825, 156171026562838, 4130464801497105, 116526877671782896, 3492868475952497313, 110856698175372359346, 3713836169709782989993
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Without the first "1" = eigensequence of triangle A003566. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Getu, S.; Shapiro, L. W.; Combinatorial view of the composition of functions. Ars Combin. 10 (1980), 131-145.
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.32(d).
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 110
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FORMULA
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n! * Sum(k=0, n, (n-k)^k/k!).
For n>=1 a(n-1)=b(n) where b(1)=1 and b(n)=sum(i=1, n-1, i*binomial(n-1, i)*b(i)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 13 2004
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MAPLE
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a := proc(n) local k; add(k^(n-k)*n!/(n-k)!, k=1..n); end; # for n >= 1
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CROSSREFS
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Cf. A072597.
A003566 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 29 2008]
Sequence in context: A158577 A006879 A163861 this_sequence A025164 A060072 A157503
Adjacent sequences: A006150 A006151 A006152 this_sequence A006154 A006155 A006156
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).
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