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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
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 19 07:31 EDT 2024. Contains 370955 sequences. (Running on oeis4.)