%I A005558 M2598
%S A005558 1,1,3,6,20,50,175,490,1764,5292,19404,60984,226512,736164,2760615,
%T A005558 9202050,34763300,118195220,449141836,1551580888,5924217936,20734762776
%N A005558 Number of walks on square lattice.
%D A005558 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005558 Heinrich Niederhausen, A Note on the Enumeration of Diffusion Walks in 
               the First Octant by Their Number of Contacts with the Diagonal, Journal 
               of Integer Sequences, Vol. 8 (2005), Article 05.4.3.
%H A005558 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 A005558 a(n) = C(n+1, ceil(n/2))*C(n, floor(n/2)) - C(n+1, ceil((n-1)/2))*C(n, 
               floor((n-1)/2)). - Paul D. Hanna (pauldhanna(AT)juno.com), Apr 16 
               2004
%F A005558 G.f. (1/(4x^2))*((16*x^2-1)*(hypergeom([1/2, 1/2],[1],16*x^2)+2*x*(4*x-1)*hypergeom([3/
               2, 3/2],[2],16*x^2))-2*x+1) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), 
               Oct 13 2009]
%o A005558 (PARI) {a(n)=binomial(n+1,ceil(n/2))*binomial(n,floor(n/2)) - binomial(n+1,
               ceil((n-1)/2))*binomial(n,floor((n-1)/2))}
%Y A005558 See A138350 for a signed version.
%Y A005558 Bisections are A000891 and A000888/2.
%Y A005558 Cf. A005559-A005562, A093768.
%Y A005558 Sequence in context: A052408 A148573 A148574 this_sequence A138350 A148575 
               A148576
%Y A005558 Adjacent sequences: A005555 A005556 A005557 this_sequence A005559 A005560 
               A005561
%K A005558 nonn
%O A005558 0,3
%A A005558 N. J. A. Sloane (njas(AT)research.att.com).