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A001372 Number of mappings (or mapping patterns) from n points to themselves; number of endofunctions.
(Formerly M2671 N1069)
+0
22
1, 1, 3, 7, 19, 47, 130, 343, 951, 2615, 7318, 20491, 57903, 163898, 466199, 1328993, 3799624, 10884049, 31241170, 89814958, 258604642, 745568756, 2152118306, 6218869389, 17988233052, 52078309200, 150899223268, 437571896993 (list; graph; listen)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pp. 41, 209.

N. G. de Bruijn, Enumeration of mapping patterns, J. Combin. Theory, 12 (1972), 14-20.

N. G. de Bruijn and D. A. Klarner, Multisets of aperiodic cycles, SIAM J, Algeb. Discrete Meth., 3 (1982), 359-368.

R. L. Davies, The numbers of structures of finite relations, Proc. Amer. Math. Soc., 4 (1953), 486-494.

S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 5.6.6.

R. A. Fisher, Contributions to Mathematical Statistics, Wiley, 1950, 41.401.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 70, Table 3.4.1.

R. C. Read, Note on number of functional digraphs, Math. Ann., vol. 143 (1961), pp. 109-111.

P. R. Stein, personal communication.

LINKS

Christian G. Bower, Table of n, a(n) for n = 0..500

F. Hivert, J.-C. Novelli and J.-Y. Thibon, Commutative combinatorial Hopf algebras

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 144

N. J. A. Sloane, Illustration of initial terms

N. J. A. Sloane, Transforms

P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 480

FORMULA

Euler transform of A002861.

MAPLE

with(combstruct): M[ 2671 ] := [ F, {F=Set(K), K=Cycle(T), T=Prod(Z, Set(T))}, unlabeled ]:

CROSSREFS

Cf. A000312, A002861, A006961, A001373, A054050, A054745.

Sequence in context: A110014 A026581 A151535 this_sequence A049117 A146810 A073063

Adjacent sequences: A001369 A001370 A001371 this_sequence A001373 A001374 A001375

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms etc. from Paul Zimmermann Mar 15 1996.

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Last modified December 1 19:22 EST 2009. Contains 167811 sequences.


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