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A032305
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Number of rooted trees where any 2 subtrees extending from the same node have a different number of nodes.
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3
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1, 1, 1, 2, 3, 6, 12, 25, 51, 111, 240, 533, 1181, 2671, 6014, 13795, 31480, 72905, 168361, 393077, 914784, 2150810, 5040953, 11914240, 28089793, 66702160, 158013093, 376777192, 896262811, 2144279852, 5120176632
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| Shifts left under "EFK" (unordered, size, unlabeled) transform.
G.f.: A(x) = x*Product_{n>=1} (1+a(n)*x^n) = Sum_{n>=1} a(n)*x^n. - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 07 2004
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MAPLE
| A:= proc(n) if n<=1 then x else convert (series (x* (product (1+ coeff (A(n-1), x, i)*x^i, i=1..n-1)), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n): seq (a(n), n=1..31); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 22 2008]
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PROG
| (PARI) a(n)=polcoeff(x*prod(i=1, n-1, 1+a(i)*x^i)+x*O(x^n), n)
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CROSSREFS
| Sequence in context: A045761 A077903 A038086 * A032218 A005829 A038087
Adjacent sequences: A032302 A032303 A032304 * A032306 A032307 A032308
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KEYWORD
| nonn
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net)
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