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%I A145603 #2 Mar 31 2012 13:47:34
%S A145603 1,35,720,12375,196625,3006003,45048640,668144880,9859090500,
%T A145603 145173803500,2136958387520,31479019635375,464342770607625,
%U A145603 6861343701121875,101583106970400000,1507019252941540800
%N A145603 a(n) is the number of walks from (0,0) to (0,4) that remain in the upper half-plane y >= 0 using 2*n +2 unit steps either up (U), down (D), left (L) or right (R).
%C A145603 Cf. A000891, which enumerates walks in the upper half-plane starting and finishing at the origin. See also A145600, A145601 and A145602. This sequence is the central column taken from the triangle A145599, which enumerates walks in the upper half-plane starting at the origin and finishing on the horizontal line y = 4.
%H A145603 R. K. Guy, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/GUY/catwalks.html">Catwalks, sandsteps and Pascal pyramids</a>, J. Integer Sequences, Vol. 3 (2000), Article #00.1.6
%F A145603 a(n) = 5/(2*n+3)*binomial(2*n+3,n+4)*binomial(2*n+3,n-1).
%p A145603 with(combinat):
%p A145603 a(n) = 5/(2*n+3)*binomial(2*n+3,n+4)*binomial(2*n+3,n-1);
%p A145603 seq(a(n),n = 1..19);
%Y A145603 A000891, A145599, A145600, A145601, A145602.
%K A145603 easy,nonn
%O A145603 1,2
%A A145603 _Peter Bala_, Oct 15 2008

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