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A004303 a(n) = C(2n-2,n-1)/n - 2^(n-1) + n.
(Formerly M3015)
0
1, 1, 1, 1, 3, 16, 75, 309, 1183, 4360, 15783, 56750, 203929, 734722, 2658071, 9662093, 35292151, 129513736, 477376575, 1766738922, 6563071865, 24464169890, 91478369359, 343051225066, 1289887370133, 4861912847046, 18367285963315, 69533416698304 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

REFERENCES

J. W. Moon, A problem on arcs without bypasses in tournaments, J. Combin. Theory B 21 (1976), 71-75.

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=1..28.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, Une méthode pour obtenir la fonction génératrice d'une série. FPSAC 1993, Florence. Formal Power Series and Algebraic Combinatorics.

FORMULA

G.f.: x + x^2*(1 - sqrt(1-4*x) - 2*x - 2*x^3/((1-x)^2 * (1-2*x)))/(2*x^2). -  Jean-François Alcover, Feb 13 2019

EXAMPLE

(n + 1) a(n) = 68 n a(n - 5) - 16 n a(n - 6) + (11 n - 2) a(n - 1) + (- 47 n + 61) a(n - 2) + (101 n - 240) a(n - 3) + (- 116 n + 398) a(n - 4) - 304 a(n - 5) + 88 a(n - 6). - Simon Plouffe, Feb 09 2012

CROSSREFS

Sequence in context: A316170 A038602 A221829 * A317365 A207836 A005947

Adjacent sequences:  A004300 A004301 A004302 * A004304 A004305 A004306

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended to a(1)=1 using formula by Alois P. Heinz, Feb 13 2019

STATUS

approved

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Last modified February 20 15:52 EST 2020. Contains 332078 sequences. (Running on oeis4.)