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A052318
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Number of labeled rooted trimmed trees with n nodes.
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15
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1, 2, 3, 16, 145, 1536, 19579, 290816, 4942305, 94689280, 2020278931, 47523053568, 1222147737265, 34117226135552, 1027550555918475, 33213871550365696, 1146891651823112641, 42135941698113503232
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A rooted trimmed tree is a tree with a forbidden limb of length 2.
A rooted tree with a forbidden limb of length k is a rooted tree where the path from any leaf inward hits a branching node or the root within k steps.
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| E.g.f. satisfies A(x)=x*exp(A(x)-x^2).
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MAPLE
| A:= proc(n) option remember; if n<=1 then x else convert (series (x* exp(A(n-1)-x^2), x, n), polynom) fi end: a:= n-> coeff (A(n+1), x, n)*n!: seq (a(n), n=1..18); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 23 2008]
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CROSSREFS
| Cf. A002955, A002988-A002992, A052319-A052329.
Sequence in context: A139802 A063666 A006247 * A141309 A179442 A057997
Adjacent sequences: A052315 A052316 A052317 * A052319 A052320 A052321
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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