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A000439 Powers of rooted tree enumerator.
(Formerly M4608 N1965)
1
9, 30, 69, 133, 230, 369, 560, 814, 1143, 1560, 2079, 2715, 3484, 4403, 5490, 6764, 8245, 9954, 11913, 14145, 16674, 19525, 22724, 26298, 30275, 34684, 39555, 44919, 50808, 57255, 64294, 71960, 80289, 89318, 99085, 109629, 120990, 133209, 146328, 160390, 175439, 191520, 208679 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
REFERENCES
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.
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
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
a(n) = (n^4 + 18*n^3 + 83*n^2 + 114*n)/24. - Philippe Deléham, Feb 13 2004
G.f.: (2*x^3 - 9*x^2 + 15*x - 9)/(x - 1)^5. - Jinyuan Wang, Mar 17 2020
MAPLE
A000439:=(2*z-3)*(z**2-3*z+3)/(z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
Table[(n^4 + 18 n^3 + 83 n^2 + 114 n) / 24, {n, 50}] (* Vincenzo Librandi, Mar 18 2020 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {9, 30, 69, 133, 230}, 50] (* Harvey P. Dale, May 15 2023 *)
PROG
(PARI) a(n) = (n^4 + 18*n^3 + 83*n^2 + 114*n)/24; \\ Jinyuan Wang, Mar 17 2020
(Magma) [(n^4 + 18*n^3 + 83*n^2 + 114*n)/24: n in [1..50]]; // Vincenzo Librandi, Mar 18 2020
(Python)
def a(n): return (n**4 + 18*n**3 + 83*n**2 + 114*n)//24
print([a(n) for n in range(1, 44)]) # Michael S. Branicky, Sep 30 2021
CROSSREFS
Sequence in context: A225275 A005919 A084370 * A002414 A273604 A273640
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Joerg Arndt, May 09 2013
STATUS
approved

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Last modified May 25 06:49 EDT 2024. Contains 372782 sequences. (Running on oeis4.)