This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A145601 #2 Mar 31 2012 13:47:34 %S A145601 1,15,189,2352,29700,382239,5010005,66745536,901995588,12342120700, %T A145601 170724392916,2384209771200,33577620944400,476432168185575, %U A145601 6805332732133125,97790670976838400,1412830549632694500 %N A145601 a(n) is the number of walks from (0,0) to (0,2) that remain in the upper half-plane y >= 0 using 2*n unit steps either up (U), down (D), left (L) or right (R). %C A145601 Cf. A000891, which enumerates walks in the upper half-plane starting and finishing at the origin. See also A145600, A145602 and A145603. This sequence is the central column taken from triangle A145597, which enumerates walks in the upper half-plane starting at the origin and finishing on the horizontal line y = 2. %H A145601 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 A145601 a(n) = 3/(2*n+1)*binomial(2*n+1,n+2)*binomial(2*n+1,n-1). %e A145601 a(2) = 15: the 15 walks from (0,0) to (0,2) of four steps are: %e A145601 UUUD, UULR, UURL, UUDU, URUL, ULUR, URLU, ULRU,RUUL, LUUR, %e A145601 RLUU, LRUU, RULU, LURU and UDUU. %p A145601 with(combinat): %p A145601 a(n) = 3/(2*n+1)*binomial(2*n+1,n+2)*binomial(2*n+1,n-1); %p A145601 seq(a(n),n = 1..19); %Y A145601 A000891, A145597, A145600, A145602, A145603. %K A145601 easy,nonn %O A145601 1,2 %A A145601 _Peter Bala_, Oct 15 2008