This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 EXTENSIONS More terms from Vladeta Jovovic, Apr 07 2001 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.