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A036249
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Number of rooted trees of nonempty sets with n points. (Each node is a set of 1 or more points.)
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5
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0, 1, 2, 5, 13, 37, 108, 332, 1042, 3360, 11019, 36722, 123875, 422449, 1453553, 5040816, 17599468, 61814275, 218252584, 774226549, 2758043727, 9862357697, 35387662266, 127374191687, 459783039109, 1664042970924, 6037070913558
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Index entries for sequences related to rooted trees
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 768
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FORMULA
| G.f. satisfies: A(x) = x*exp( Sum_{n>=1} (A(x^n) + x^n)/n ). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 19 2005
If b(n) is the Euler transform of a(n), then a(n+1) = a(n) + b(n). - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 09 2006
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PROG
| (PARI) {a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x*exp(sum(m=1, n, (subst(A, x, x^m)+x^m)/m))); polcoeff(A, n, x)} (Hanna)
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CROSSREFS
| Essentially the same as A029856. Cf. A048802.
Sequence in context: A092395 A019268 A005961 * A126031 A151416 A193114
Adjacent sequences: A036246 A036247 A036248 * A036250 A036251 A036252
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Nov 15 1998.
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