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Search: id:A063881
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| A063881 |
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Number of oriented trees rooted at an arc. |
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+0
1
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| 1, 4, 18, 80, 367, 1708, 8122, 39204, 191963, 950984, 4759626, 24030736, 122258314, 626162464, 3225926450, 16706775984, 86928097451, 454203897192, 2382255252398, 12537764465072, 66193294753768, 350472816969976
(list; graph; listen)
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OFFSET
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2,2
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REFERENCES
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F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 61, (3.3.7).
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FORMULA
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a(n) = A000151(n)- A000238(n). G.f.: A(x) = B(x)^2, where B(x) is g.f. for A000151.
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MAPLE
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B:= proc(n) option remember; if n<=1 then unapply(x, x) else unapply (convert (series (x*exp (2*sum (B(n-1)(x^k)/k, k=1..n-1)), x, n+1), polynom), x) fi end: a:= proc(n) local T; T:=B(n-1)(x); add (coeff (T, x, k)* coeff(T, x, n-k), k=1..n-1) end: seq (a(n), n=2..23); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 23 2008]
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CROSSREFS
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Cf. A000151, A000238.
Sequence in context: A090017 A104631 A106391 this_sequence A100192 A052913 A129160
Adjacent sequences: A063878 A063879 A063880 this_sequence A063882 A063883 A063884
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 27 2001
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