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A339525
Number of unordered pairs of rooted trees with a total of n nodes and an odd total of leaves.
2
0, 0, 0, 1, 3, 8, 19, 47, 119, 309, 805, 2115, 5594, 14920, 40037, 108068, 293124, 798739, 2185380, 6001797, 16538728, 45716315, 126727586, 352214041, 981269274, 2739925455, 7666335708, 21491822234, 60358497108, 169798015580, 478420350367
OFFSET
1,5
COMMENTS
Equivalently, the number of rooted trees on n+1 nodes, where the root has degree 2, and the number of leaves is odd.
To get a pair of trees with an odd number of leaves one tree must have an even number of leaves and the other an odd number of leaves.
FORMULA
a(n) = Sum_{k=1, n-1}( A253013(k) * A253014(n-k) ).
CROSSREFS
KEYWORD
nonn
AUTHOR
Washington Bomfim, Dec 08 2020
STATUS
approved