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A058300
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Number of ways of piling up n wine bottles above a row of n+1 bottles at ground level.
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0
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1, 1, 1, 3, 7, 16, 43, 115, 303, 813, 2203, 5991, 16371, 44917, 123598, 340988, 942930, 2612735, 7252407, 20163046, 56136326, 156488946, 436739752, 1220157514, 3412116339, 9550192161
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Related to the Catalan numbers (which count the ways of storing an arbitrary number of bottles above n bottles at ground level).
Related to fountains of n coins (A005169) [Joerg Arndt, Mar 18 2011].
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REFERENCES
| R. P. Stanley: Enumerative Combinatorics (Volume 2); see Exercise 6.19(hhh).
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FORMULA
| Coefficient of w^(2*n+1)*z^(n+1) in the formal power series G(w, z) defined by G(w, z)=1+w*z*G(w, w*z)
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EXAMPLE
| a(4) = 7: the seven possibilities are:
..............0.............0.........0...............0.........0............0
.0.0.0.0.....0.0.0.......0.0.0.......0.0...0.....0...0.0.......0.0.0......0.0.0
0.0.0.0.0.,.0.0.0.0.0.,.0.0.0.0.0.,.0.0.0.0.0.,.0.0.0.0.0.,.0.0.0.0.0,.0.0.0.0.0
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CROSSREFS
| Sequence in context: A036567 A018023 A144977 * A000674 A129045 A005312
Adjacent sequences: A058297 A058298 A058299 * A058301 A058302 A058303
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KEYWORD
| easy,nonn,nice
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AUTHOR
| Roland Bacher (Roland.Bacher(AT)ujf-grenoble.fr), Dec 08 2000
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