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A005719
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Quadrinomial coefficients.
(Formerly M2019)
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3
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2, 12, 40, 101, 216, 413, 728, 1206, 1902, 2882, 4224, 6019, 8372, 11403, 15248, 20060, 26010, 33288, 42104, 52689, 65296, 80201, 97704, 118130, 141830, 169182, 200592, 236495, 277356, 323671, 375968, 434808, 500786, 574532, 656712, 748029, 849224, 961077
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OFFSET
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2,1
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REFERENCES
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L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
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=2..39.
R. K. Guy, Letter to N. J. A. Sloane, 1987
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.
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FORMULA
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a(n)= binomial(n, 2)*(n^3+11*n^2+46*n-24)/60, n >= 2.
G.f.: (x^2)*(2-2*x^2+x^3)/(1-x)^6 (numerator polynomial is N4(5, x) from A063421.)
a(n) = 2*binomial(n,2) + 6*binomial(n,3) + 4*binomial(n,4) + binomial(n,5) (see comment in A071675). - Vladimir Shevelev and Peter J. C. Moses, Jun 22 2012
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MAPLE
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A005719:=(2-2*z**2+z**3)/(z-1)**6; [Conjectured by Simon Plouffe in his 1992 dissertation.]
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CROSSREFS
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a(n)= A008287(n, 5), n >= 2 (sixth column of quadrinomial coefficients).
Sequence in context: A168057 A290131 A008911 * A143126 A118417 A069144
Adjacent sequences: A005716 A005717 A005718 * A005720 A005721 A005722
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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