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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

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, 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,changed

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 26 17:22 EST 2021. Contains 341632 sequences. (Running on oeis4.)