A121398 Main diagonal of triangle A121400; also equals the partial sums of column 0 (A121399) of the same triangle.
1, 2, 5, 11, 28, 70, 184, 486, 1313, 3576, 9851, 27319, 76286, 214120, 603858, 1709719, 4857959, 13845948, 39572583, 113380652, 325576692, 936796592, 2700456452, 7797587816, 22550434989, 65308288346, 189388557677
Offset: 0
Keywords
Programs
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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)}
Formula
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).