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%I #17 Jul 22 2020 18:32:06
%S 1,1,1,3,5,13,29,71,165,421,1029,2647,6593,17241,43801,115555,297513,
%T 791337,2062737,5516755,14497373,38994597,103269053,278921927,
%U 742950845,2014648253,5396210357,14677306503,39477832745,107701409665,290871580345,795431700707,2155140605137
%N Number of unlabelled unary-binary trees with n nodes such that every node with two children has children of different subtree sizes.
%F a(1) = 1, a(n) = a(n-1) + Sum_{k=1..n-2} (a(k)*a(n-k-1)*[k != n-k-1]).
%o (PARI) lista(nn) = {my(va = vector(nn)); va[1] = 1; for (n=2, nn, va[n] = va[n-1] + sum(k=1, n-2, if (k != n-k-1, va[k]*va[n-k-1]));); va;} \\ _Michel Marcus_, Jun 14 2020
%Y Cf. A000992.
%K nonn
%O 1,4
%A _Marcel K. Goh_, Jun 14 2020
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