Search: id:A001372
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%I A001372 M2671 N1069
%S A001372 1,1,3,7,19,47,130,343,951,2615,7318,20491,57903,163898,466199,1328993,
%T A001372 3799624,10884049,31241170,89814958,258604642,745568756,2152118306,
%U A001372 6218869389,17988233052,52078309200,150899223268,437571896993
%N A001372 Number of mappings (or mapping patterns) from n points to themselves; 
               number of endofunctions.
%D A001372 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001372 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001372 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like 
               Structures, Cambridge, 1998, pp. 41, 209.
%D A001372 N. G. de Bruijn, Enumeration of mapping patterns, J. Combin. Theory, 
               12 (1972), 14-20.
%D A001372 N. G. de Bruijn and D. A. Klarner, Multisets of aperiodic cycles, SIAM 
               J, Algeb. Discrete Meth., 3 (1982), 359-368.
%D A001372 R. L. Davies, The numbers of structures of finite relations, Proc. Amer. 
               Math. Soc., 4 (1953), 486-494.
%D A001372 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.6.
%D A001372 R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 
               41.401.
%D A001372 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 
               1973, p. 70, Table 3.4.1.
%D A001372 R. C. Read, Note on number of functional digraphs, Math. Ann., vol. 143 
               (1961), pp. 109-111.
%D A001372 P. R. Stein, personal communication.
%H A001372 Christian G. Bower, <a href="b001372.txt">Table of n, a(n) for n = 0..500</
               a>
%H A001372 F. Hivert, J.-C. Novelli and J.-Y. Thibon, <a href="http://arXiv.org/
               abs/math.CO/0605262">Commutative combinatorial Hopf algebras</a>
%H A001372 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=144">
               Encyclopedia of Combinatorial Structures 144</a>
%H A001372 N. J. A. Sloane, <a href="a1372.gif">Illustration of initial terms</a>
%H A001372 N. J. A. Sloane, <a href="transforms.txt">Transforms</a>
%H A001372 P. Flajolet and R. Sedgewick, <a href="http://algo.inria.fr/flajolet/
               Publications/books.html">Analytic Combinatorics</a>, 2009; see page 
               480
%F A001372 Euler transform of A002861.
%p A001372 with(combstruct): M[ 2671 ] := [ F,{F=Set(K), K=Cycle(T), T=Prod(Z,Set(T))},
               unlabeled ]:
%Y A001372 Cf. A000312, A002861, A006961, A001373, A054050, A054745.
%Y A001372 Sequence in context: A110014 A026581 A151535 this_sequence A049117 A146810 
               A073063
%Y A001372 Adjacent sequences: A001369 A001370 A001371 this_sequence A001373 A001374 
               A001375
%K A001372 nonn,nice,easy
%O A001372 0,3
%A A001372 N. J. A. Sloane (njas(AT)research.att.com).
%E A001372 More terms etc. from Paul Zimmermann Mar 15 1996.

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