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A145602 a(n) is the number of walks from (0,0) to (0,3) that remain in the upper half-plane y >= 0 using 2*n +1 unit steps either up (U), down (D), left (L) or right (R). 5
1, 24, 392, 5760, 81675, 1145144, 16032016, 225059328, 3173688180, 44986664800, 641087516256, 9183622822400, 132211882468575, 1912322889603000, 27781440618420000, 405248874740582400, 5933888308457316900 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Cf. A000891, which enumerates walks in the upper half-plane starting and finishing at the origin. See also A145600, A145601 and A145603. This sequence is the central column taken from the triangle A145598, which enumerates walks in the upper half-plane starting at the origin and finishing on the horizontal line y = 3.
LINKS
R. K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6
FORMULA
a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1).
MAPLE
with(combinat):
a(n) = 2/(n+1)*binomial(2*n+2, n+3)*binomial(2*n+2, n-1);
seq(a(n), n = 1..19);
CROSSREFS
Sequence in context: A022448 A025947 A007752 * A020447 A021894 A021694
KEYWORD
easy,nonn
AUTHOR
Peter Bala, Oct 15 2008
STATUS
approved

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Last modified March 19 01:57 EDT 2024. Contains 370952 sequences. (Running on oeis4.)