A000551 Number of labeled rooted trees of height 2 with n nodes. (Formerly M4220 N1764)

6, 36, 200, 1170, 7392, 50568, 372528, 2936070, 24617120, 218521116, 2045278248, 20112821274, 207162957120, 2228888801040, 24989309310944, 291322555295886, 3524580202643136, 44176839081266340, 572725044269255640

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.

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

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: A374497 A345340 A232138 * A038157 A267468 A225685

Adjacent sequences: A000548 A000549 A000550 * A000552 A000553 A000554

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Flajolet and Zimmermann, Mar 15 1996

Status

approved