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 A005719 Quadrinomial coefficients. (Formerly M2019) 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 REFERENCES 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). LINKS 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; arXiv:0911.4975 [math.NT], 2009. Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992 FORMULA 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 MAPLE A005719:=(2-2*z**2+z**3)/(z-1)**6; [Conjectured by Simon Plouffe in his 1992 dissertation.] CROSSREFS 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 KEYWORD nonn AUTHOR STATUS approved

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Last modified July 4 11:57 EDT 2022. Contains 355075 sequences. (Running on oeis4.)