A182017 - OEIS

%I #9 Oct 15 2024 20:28:49

%S 1,5,29,165,1020,6606,44805,314299,2266834,16714004,125501364,

%T 956725836,7387322749,57669478609,454492588153,3611698593169,

%U 28911762536992,232949503809562,1887883708627582,15380196764853214,125893997550676627,1034945699861044243

%N Row square-sums of triangle A182013.

%F a(n) = Sum_{k=0..n} (Sum_{i=k..n} M(i))^2, where the M(n)'s are the Motzkin numbers (A001006).

%t M[n_]:=If[n==0,1,Coefficient[(1+x+x^2)^(n+1),x^n]/(n+1)]; Table[Sum[Sum[M[i],{i,k,n}]^2,{k,0,n}],{n,0,40}]

%o (Maxima) M(n):=coeff(expand((1+x+x^2)^(n+1)),x^n)/(n+1);

%o makelist(sum(sum(M(i),i,k,n)^2,k,0,n),n,0,20);

%Y Cf. A001006, A182013.

%K nonn

%O 0,2

%A _Emanuele Munarini_, Apr 06 2012