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Number of unordered pairs of rooted trees with a total of n nodes and an even total of leaves.
2

%I #20 Dec 21 2020 15:36:25

%S 0,1,1,2,3,8,18,49,120,313,802,2120,5591,14942,40033,108108,293094,

%T 798839,2185341,6002085,16538599,45716952,126727195,352215812,

%U 981268481,2739930091,7666333161,21491833976,60358490615,169798048026,478420333601

%N Number of unordered pairs of rooted trees with a total of n nodes and an even total of leaves.

%C Equivalently, the number of rooted trees on n+1 nodes, where the root has degree 2, and the number of leaves is even.

%H Washington Bomfim, <a href="/A339524/a339524_1.png">Illustration of initial terms</a>

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%F a(n) = A027852(n) - A339525(n).

%Y Cf. A027852, A339525.

%K nonn

%O 1,4

%A _Washington Bomfim_, Dec 08 2020