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%I #6 Feb 28 2022 07:51:45
%S 1,1,1,1,2,6,16,37,114,478,1907,6777,28414,148580,758930,3580294,
%T 18982050,117888762,720679726,4193516446,26798335830,191775198574,
%U 1353198262531,9303932353127,69303156652024,559295471922890,4454686099742810,35198016469190740
%N a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1,3*k) * a(k) * a(n-3*k-1).
%F E.g.f.: exp( Sum_{n>=0} a(n) * x^(3*n+1) / (3*n+1)! ).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 3 k] a[k] a[n - 3 k - 1], {k, 0, Floor[(n - 1)/3]}]; Table[a[n], {n, 0, 27}]
%Y Cf. A138314, A351969.
%K nonn
%O 0,5
%A _Ilya Gutkovskiy_, Feb 26 2022
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