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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 Vincenzo Librandi, Table of n, a(n) for n = 3..200 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: A055299 A261520 A232138 * A038157 A267468 A225685 Adjacent sequences:  A000548 A000549 A000550 * A000552 A000553 A000554 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from Flajolet and Zimmermann, Mar 15 1996 STATUS approved

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)