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A000949 Number of forests with n nodes and height at most 2.
(Formerly M3021 N1223)
30
1, 1, 3, 16, 101, 756, 6607, 65794, 733833, 9046648, 121961051, 1782690174, 28055070397, 472594822324, 8479144213191, 161340195463066, 3243707386310033, 68679247688467056, 1526976223741111987, 35557878951515668726, 865217354118762606021 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Equivalently, the number of mappings from a set of n elements into itself where f(f(x)) = f(f(f(x))). - Chad Brewbaker, Mar 26 2014

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

T. D. Noe, Table of n, a(n) for n = 0..100

J. Riordan, Forests of labeled trees, J. Combin. Theory, 5 (1968), 90-103.

FORMULA

E.g.f.: exp(x*exp(x*exp(x))).

a(n) = n!*sum(m=1..n-1, sum(k=1..n-m, (k^(n-m-k)*m^k)/(k!*(n-m-k)!))/m!)+1. - Vladimir Kruchinin, May 28 2011

MATHEMATICA

nn = 20; Range[0, nn]! CoefficientList[Series[Exp[x*Exp[x*Exp[x]]], {x, 0, nn}], x] (* T. D. Noe, Jun 21 2012 *)

PROG

(Maxima) a(n):=n!*sum(sum((k^(n-m-k)*m^k)/(k!*(n-m-k)!), k, 1, n-m)/m!, m, 1, n-1)+1; /* Vladimir Kruchinin, May 28 2011 */

(PARI) x='x+O('x^66); Vec(serlaplace(exp(x*exp(x*exp(x))))) /* show terms with a(0)=1 */ /* Joerg Arndt, May 28 2011 */

CROSSREFS

Cf. A000248, A000950, A000951, A052512-A052514.

Column k=2 of A210725. - Alois P. Heinz, Mar 15 2013

Sequence in context: A137572 A009151 A009007 * A091637 A278429 A207434

Adjacent sequences:  A000946 A000947 A000948 * A000950 A000951 A000952

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Apr 07 2001

STATUS

approved

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Last modified November 20 10:31 EST 2017. Contains 294963 sequences.