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%I #2 Mar 31 2012 13:47:34
%S 1,24,392,5760,81675,1145144,16032016,225059328,3173688180,
%T 44986664800,641087516256,9183622822400,132211882468575,
%U 1912322889603000,27781440618420000,405248874740582400,5933888308457316900
%N 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).
%C 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.
%H 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 a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1).
%p with(combinat):
%p a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1);
%p seq(a(n),n = 1..19);
%Y A000891, A145598, A145600, A145601, A145603.
%K easy,nonn
%O 1,2
%A _Peter Bala_, Oct 15 2008