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%I #6 Apr 09 2012 11:56:43
%S 1,3,15,85,531,3545,24833,180251,1344163,10237001,79287469,622596063,
%T 4945078477,39658283943,320689293119,2611817435525,21405148148051,
%U 176396318594937,1460795339822349,12150467810552223,101463416752305385,850306144532133787
%N Central coefficients of triangle A182013.
%F a(n) = sum(M(i),i=n..2*n), where the M(n)'s are the Motzkin numbers.
%F Recurrence: a(n+1) = a(n) + M(2n+2) + M(2n+1) - M(n).
%t M[n_]:=If[n==0,1,Coefficient[(1+x+x^2)^(n+1),x^n]/(n+1)]; Table[Sum[M[i],{i,n,2n}],{n,0,40}]
%o (Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)),x^n)/(n+1);
%o makelist(sum(M(i),i,n,2*n),n,0,20);
%K nonn
%O 0,2
%A _Emanuele Munarini_, Apr 06 2012