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A005719 Quadrinomial coefficients.
(Formerly M2019)
3

%I M2019

%S 2,12,40,101,216,413,728,1206,1902,2882,4224,6019,8372,11403,15248,

%T 20060,26010,33288,42104,52689,65296,80201,97704,118130,141830,169182,

%U 200592,236495,277356,323671,375968,434808,500786,574532,656712,748029,849224,961077

%N Quadrinomial coefficients.

%D L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.

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

%H R. K. Guy, <a href="/A005712/a005712.pdf">Letter to N. J. A. Sloane, 1987</a>

%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.

%F a(n)= binomial(n, 2)*(n^3+11*n^2+46*n-24)/60, n >= 2.

%F G.f.: (x^2)*(2-2*x^2+x^3)/(1-x)^6 (numerator polynomial is N4(5, x) from A063421.)

%F 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

%p A005719:=(2-2*z**2+z**3)/(z-1)**6; [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]

%Y a(n)= A008287(n, 5), n >= 2 (sixth column of quadrinomial coefficients).

%K nonn

%O 2,1

%A _N. J. A. Sloane_.

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Last modified February 15 16:53 EST 2019. Contains 320136 sequences. (Running on oeis4.)