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A000551
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Number of labeled rooted trees of height 2 with n nodes.
(Formerly M4220 N1764)
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5
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6, 36, 200, 1170, 7392, 50568, 372528, 2936070, 24617120, 218521116, 2045278248, 20112821274, 207162957120, 2228888801040, 24989309310944, 291322555295886, 3524580202643136, 44176839081266340, 572725044269255640
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OFFSET
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3,1
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REFERENCES
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N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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MAPLE
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# ht(m) counts trees of height<=m; ht := proc(m) local i; [ T0, {seq(T.i=Prod(Z, Set(T.(i+1))), i=0..m-1), T.m=Z}, labeled ] end: M[ 4220 ] := n->count(ht(2), size=n)-count(ht(1), size=n): seq(M[ 4220 ](n), n=3..21);
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MATHEMATICA
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a[n_] = n*(n-1)*Sum[k^(n-2-k)*Binomial[n-2, k-1], {k, n-2}]; Table[a[n], {n, 3, 21}] (* Jean-François Alcover, Jun 29 2011, after formula *)
With[{nn=30}, Drop[CoefficientList[Series[x (Exp[x Exp[x]]-Exp[x]), {x, 0, nn}], x] Range[0, nn]!, 3]] (* Harvey P. Dale, Apr 17 2017 *)
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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More terms from Flajolet and Zimmermann, Mar 15 1996
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STATUS
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approved
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