This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382440 #13 Apr 04 2025 15:14:32
%S A382440 1,1,2,3,6,11,23,45,95,194,414,863,1850,3910,8413,17887,38517,82249,
%T A382440 177133,378871,815265,1745006,3750385,8024725,17219142,36817113
%N A382440 Number of rooted full binary trees with n internal nodes, up to their multiset of subtree sizes.
%C A382440 The multiset of subtree sizes of a binary tree T is the multiset containing the number of internal nodes of the subtrees rooted at each internal node of T.
%C A382440 Isomorphic binary trees have the same multiset of subtree sizes. More precisely, binary trees giving rectangle tilings with the same shapes (cf. A247139) have the same multiset of subtree sizes.
%e A382440 The following binary tree has its multiset of subtree sizes equal to {4, 3, 1, 1}:
%e A382440 o
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%e A382440 o o \
%e A382440 / \ / \ \
%e A382440 o o o o o
%e A382440 The 6 multisets of subtree sizes corresponding to a(5) = 6 are:
%e A382440 {5, 3, 1, 1, 1}, {5, 2, 2, 1, 1}, {5, 3, 2, 1, 1},
%e A382440 {5, 4, 2, 1, 1}, {5, 4, 3, 1, 1}, {5, 4, 3, 2, 1}.
%Y A382440 Cf. A000108, A001190, A247139.
%K A382440 nonn,more
%O A382440 1,3
%A A382440 _Ludovic Schwob_, Mar 25 2025