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A029856
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Number of rooted trees with 2-colored leaves.
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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, 6037070913558, 21951214425140, 79981665585029
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refs;
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OFFSET
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1,1
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..1000
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, 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); # Alois P. Heinz, Aug 22 2008
# even more efficient:
with (numtheory): a:= proc(n) option remember; local d, j; if n<=1 then 2*n else (add (d*a(d), d=divisors(n-1)) +add (add (d*a(d), d=divisors(j)) *a(n-j), j=1..n-2))/ (n-1) fi end: seq (a(n), n=1..25); # Alois P. Heinz, Sep 06 2008
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PROG
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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: A208175 A078413 A019083 * A072898 A032290 A032201
Adjacent sequences: A029853 A029854 A029855 * 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 G. Bower
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STATUS
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approved
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