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Search: id:A029856
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| A029856 |
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Number of rooted trees with 2-colored leaves. |
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+0
7
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| 2, 2, 5, 13, 37, 108, 332, 1042, 3360, 11019, 36722, 123875, 422449, 1453553, 5040816, 17599468, 61814275, 218252584, 774226549, 2758043727, 9862357697, 35387662266, 127374191687, 459783039109, 1664042970924
(list; graph; listen)
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OFFSET
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1,1
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 768
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees
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FORMULA
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Shifts left under Euler transform.
G.f. satisfies: A(x) = x + x*exp( Sum_{n>=1} A(x^n)/n ). - Paul D. Hanna (pauldhanna(AT)juno.com), Oct 19 2005
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MAPLE
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A:= proc(n) option remember; if n=0 then 0 else convert (series (x+x* exp (sum (subs (x=x^i, A(n-1))/i, i=1..n-1)), x=0, n+1), polynom) fi end; a:= n-> coeff (A(n), x, n): seq (a(n), n=1..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
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PROGRAM
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(PARI) {a(n)=local(A=x+x*O(x^n)); for(i=1, n, A=x+x*exp(sum(m=1, n, subst(A, x, x^m)/m))); polcoeff(A, n, x)} (Hanna)
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CROSSREFS
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Essentially the same as A036249. Cf. A000081, A029857, A038049.
Sequence in context: A095339 A078413 A019083 this_sequence A072898 A032290 A032201
Adjacent sequences: A029853 A029854 A029855 this_sequence A029857 A029858 A029859
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KEYWORD
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nonn,easy,eigen
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AUTHOR
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Christian Bower (bowerc(AT)usa.net)
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