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A000439
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Powers of rooted tree enumerator.
(Formerly M4608 N1965)
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1
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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)
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OFFSET
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1,1
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REFERENCES
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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).
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LINKS
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Table of n, a(n) for n=1..43.
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
Index entries for sequences related to rooted trees
Index entries for sequences related to trees
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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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
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MAPLE
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A000439:=(2*z-3)*(z**2-3*z+3)/(z-1)**5; # conjectured by Simon Plouffe in his 1992 dissertation
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MATHEMATICA
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Table[(n^4 + 18 n^3 + 83 n^2 + 114 n) / 24, {n, 50}] (* Vincenzo Librandi, Mar 18 2020 *)
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PROG
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(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
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CROSSREFS
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Sequence in context: A225275 A005919 A084370 * A002414 A273604 A273640
Adjacent sequences: A000436 A000437 A000438 * A000440 A000441 A000442
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Joerg Arndt, May 09 2013
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STATUS
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approved
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