Search: id:A036777
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%I A036777
%S A036777 1,2,9,64,625,7776,117642,2096752,43030008,999357660,25912953990,
%T A036777 742054808880,23259517076796,792084372215136,29120668067951460,
%U A036777 1149560690861943360,48497162427675081120,2177517061087611122880
%N A036777 Number of labeled rooted trees with a degree constraint.
%C A036777 Let A be a finite set of size n. Then a(n) is the number of binary relations 
               on A that are also functions. Note that a(n)=sum(binomial(n,k)*n^k, 
               k=0..n)=(n+1)^n, where binomial(n,k) is the number of ways to select 
               a domain D of size k from A and n^k is the number of functions from 
               D to A. - Dennis P. Walsh (dwalsh(AT)mtsu.edu), Mar 13 2006
%C A036777 For example, a(2)=9 because there are exactly 9 binary relations on A={1, 
               2} that are functions, namely: {}, {(1,1)}, {(1,2)}, {(2,1)}, {(2,
               2)}, {(1,1),(2,1)}, {(1,1),(2,2)}, {(1,2),(2,1)} and {(1,2),(2,2)}. 
               - Dennis P. Walsh (dwalsh(AT)mtsu.edu), Mar 13 2006
%D A036777 L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 
               (1993), 1-10, esp. Eq. (14) with r = 5.
%H A036777 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%F A036777 a(n)=sum(binomial(n,k)*n^k,k=0..n)=(n+1)^n - Dennis P. Walsh (dwalsh(AT)mtsu.edu), 
               Mar 13 2006
%Y A036777 Sequence in context: A128577 A052514 A036776 this_sequence A000169 A055860 
               A152917
%Y A036777 Adjacent sequences: A036774 A036775 A036776 this_sequence A036778 A036779 
               A036780
%K A036777 nonn
%O A036777 0,2
%A A036777 N. J. A. Sloane (njas(AT)research.att.com).

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