%I A005566 M1627
%S A005566 1,2,6,18,60,200,700,2450,8820,31752,116424,426888,1585584,5889312,
%T A005566 22084920,82818450,312869700,1181952200,4491418360,17067389768,
%U A005566 65166397296,248817153312,953799087696,3656229836168,14062422446800
%N A005566 Number of walks of length n on square lattice, starting at origin, staying 
               in first quadrant.
%C A005566 Contribution from Eric Egge (eegge(AT)carleton.edu), Oct 21 2008: (Start)
%C A005566 a(n) is the number of involutions of length 2n which are invariant
%C A005566 under the reverse-complement map and have no decreasing subsequences
%C A005566 of length 5. (End)
%D A005566 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005566 R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">J. Integer Seqs., Vol. 3 (2000), #00.1.6</
               a>
%F A005566 a(n) = binomial(n, [n/2])*binomial(n+1, [(n+1)/2])
%F A005566 E.g.f.: (BesselI(0, 2*x)+BesselI(1, 2*x))^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Apr 28 2003
%F A005566 EXPCONV of A001405 with itself, i.e. a(n) = sum_{k=0}^n binomial(n,k)*A001405(k)*A001405(n-k) 
               - Max Alekseyev (maxale(AT)gmail.com), May 18 2006
%F A005566 (16*x^2-1)*hypergeom([3/2, 3/2],[2],16*x^2)+(1/(2x)+2)*hypergeom([1/2, 
               1/2],[1],16*x^2)-1/(2x) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), 
               Oct 13 2009]
%Y A005566 Cf. A001700, A060897-A060900.
%Y A005566 a(2*n) = A000894(n), a(2*n+1) = 2*A060150(n+1).
%Y A005566 Sequence in context: A148460 A148461 A002527 this_sequence A005631 A118677 
               A150043
%Y A005566 Adjacent sequences: A005563 A005564 A005565 this_sequence A005567 A005568 
               A005569
%K A005566 nonn
%O A005566 0,2
%A A005566 N. J. A. Sloane (njas(AT)research.att.com).
%E A005566 Additional comments from David W. Wilson (davidwwilson(AT)comcast.net), 
               May 05 2001