A335562 Number of unlabelled unary-binary trees with n nodes such that every node with two children has children of different subtree sizes.

1, 1, 1, 3, 5, 13, 29, 71, 165, 421, 1029, 2647, 6593, 17241, 43801, 115555, 297513, 791337, 2062737, 5516755, 14497373, 38994597, 103269053, 278921927, 742950845, 2014648253, 5396210357, 14677306503, 39477832745, 107701409665, 290871580345, 795431700707, 2155140605137

Offset: 1

Author

Marcel K. Goh, Jun 14 2020

Keywords

• nonn

Crossrefs

Cf. A000992.

Programs

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

Formula

a(1) = 1, a(n) = a(n-1) + Sum_{k=1..n-2} (a(k)*a(n-k-1)*[k != n-k-1]).