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A001372 Number of mappings (or mapping patterns) from n points to themselves; number of endofunctions.
(Formerly M2671 N1069)
24
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; refs; listen; history; internal format)
OFFSET

0,3

REFERENCES

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. Davis, 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.

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

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

P. R. Stein, personal communication.

LINKS

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

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

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

FORMULA

Euler transform of A002861.

MAPLE

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

a:=seq(count(M[2671], size=n), n=0..27);

CROSSREFS

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

Sequence in context: A026581 A151535 A181360 * A179467 A049117 A146810

Adjacent sequences:  A001369 A001370 A001371 * 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. Added line to the Maple code to show how to obtain the output by W. Edwin Clark Nov. 23, 2010.

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Last modified February 16 14:07 EST 2012. Contains 205930 sequences.