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A000551 Number of labeled rooted trees of height 2 with n nodes.
(Formerly M4220 N1764)
5
6, 36, 200, 1170, 7392, 50568, 372528, 2936070, 24617120, 218521116, 2045278248, 20112821274, 207162957120, 2228888801040, 24989309310944, 291322555295886, 3524580202643136, 44176839081266340, 572725044269255640 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
REFERENCES
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).
LINKS
J. Riordan, Enumeration of trees by height and diameter, IBM J. Res. Dev. 4 (1960), 473-478.
FORMULA
E.g.f.: x*(exp(x*exp(x))-exp(x)), cf. A074728. - Vladeta Jovovic, Jan 29 2008
a(n) = n*(n-1)*A074728(n-2). - Sean A. Irvine, Nov 21 2010
MAPLE
# 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);
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A261520 A345340 A232138 * A038157 A267468 A225685
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from Flajolet and Zimmermann, Mar 15 1996
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)