cp's OEIS Frontend

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).

%I A145602 #2 Mar 31 2012 13:47:34
%S A145602 1,24,392,5760,81675,1145144,16032016,225059328,3173688180,
%T A145602 44986664800,641087516256,9183622822400,132211882468575,
%U A145602 1912322889603000,27781440618420000,405248874740582400,5933888308457316900
%N 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).
%C A145602 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 A145602 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 A145602 a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1).
%p A145602 with(combinat):
%p A145602 a(n) = 2/(n+1)*binomial(2*n+2,n+3)*binomial(2*n+2,n-1);
%p A145602 seq(a(n),n = 1..19);
%Y A145602 A000891, A145598, A145600, A145601, A145603.
%K A145602 easy,nonn
%O A145602 1,2
%A A145602 _Peter Bala_, Oct 15 2008