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%I #3 Mar 30 2012 18:36:58
%S 1,2,5,11,28,70,184,486,1313,3576,9851,27319,76286,214120,603858,
%T 1709719,4857959,13845948,39572583,113380652,325576692,936796592,
%U 2700456452,7797587816,22550434989,65308288346,189388557677
%N Main diagonal of triangle A121400; also equals the partial sums of column 0 (A121399) of the same triangle.
%F G.f. A(x) = A(x^2*G)*G*(1-x^2*G)/(1-x), where G(x) is the g.f. of the Motzkin numbers (A001006): G = (1 + x*G + x^2*G^2).
%o (PARI) {a(n)=local(F=1+x+x^2,G=serreverse(x/(F+x^2*O(x^n)))/x,H=1+x,A); for(i=0,n,H=G*subst(H,x,x^2*G)+x^2*O(x^n)); A=(x*H-y*subst(H,x,x*y))/(x*subst(F,x,y)-y); polcoeff(polcoeff(A,n,x),n,y)}
%Y Cf. A121400 (triangle), A121399 (column 0), A001006 (Motzkin).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 27 2006
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