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A030033 a(n+1) = Sum_{k = 0..floor(2*n/3)} a(k)*a(n-k) for n >= 0 with a(0) = 1.

%I A030033 #17 Oct 15 2021 08:38:45
%S A030033 1,1,1,2,4,7,15,34,72,165,387,861,2039,4894,11256,27085,66021,156347,
%T A030033 381720,940211,2261208,5578659,13846756,33654950,83539418,208608556,
%U A030033 512069441,1278522424,3207377196,7925966000
%N A030033 a(n+1) = Sum_{k = 0..floor(2*n/3)} a(k)*a(n-k) for n >= 0 with a(0) = 1.
%H A030033 Seiichi Manyama, <a href="/A030033/b030033.txt">Table of n, a(n) for n = 0..1000</a>
%p A030033 a := proc(n) local k; option remember;
%p A030033      if n = 0 then 1;
%p A030033      else add(a(k)*a(n - 1 - k), k = 0 .. floor(2/3*n - 2/3));
%p A030033      end if;
%p A030033 end proc;
%p A030033 seq(a(n), n = 0..30); # _Petros Hadjicostas_, Nov 07 2019
%Y A030033 Cf. A000992, A030032, A030037.
%K A030033 nonn
%O A030033 0,4
%A A030033 _N. J. A. Sloane_
%E A030033 Name edited by _Petros Hadjicostas_, Nov 07 2019