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A000439 Powers of rooted tree enumerator.
(Formerly M4608 N1965)
1

%I M4608 N1965

%S 9,30,69,133,230,369,560,814,1143,1560,2079,2715,3484,4403,5490,6764,

%T 8245,9954,11913,14145,16674,19525,22724,26298,30275,34684,39555,

%U 44919,50808,57255,64294,71960,80289,89318,99085,109629,120990,133209,146328,160390,175439,191520,208679

%N Powers of rooted tree enumerator.

%D J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (n^4 + 18*n^3 + 83*n^2 + 114*n)/24. - _Philippe Deléham_, Feb 13 2004

%F G.f.: (2*x^3 - 9*x^2 + 15*x - 9)/(x - 1)^5. - _Jinyuan Wang_, Mar 17 2020

%p A000439:=(2*z-3)*(z**2-3*z+3)/(z-1)**5; # conjectured by _Simon Plouffe_ in his 1992 dissertation

%t Table[(n^4 + 18 n^3 + 83 n^2 + 114 n) / 24, {n, 50}] (* _Vincenzo Librandi_, Mar 18 2020 *)

%o (PARI) a(n) = (n^4 + 18*n^3 + 83*n^2 + 114*n)/24; \\ _Jinyuan Wang_, Mar 17 2020

%o (MAGMA) [(n^4 + 18*n^3 + 83*n^2 + 114*n)/24: n in [1..50]]; // _Vincenzo Librandi_, Mar 18 2020

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Joerg Arndt_, May 09 2013

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Last modified August 11 23:04 EDT 2020. Contains 336434 sequences. (Running on oeis4.)