login
a(n) is the number of cycles of the permutation that converts forest(n) of depth-first planar planted binary trees into breadth-first representation.
4

%I #9 May 23 2022 04:01:46

%S 1,2,3,6,10,12,17,26,34,50,56,68,82,94,113

%N a(n) is the number of cycles of the permutation that converts forest(n) of depth-first planar planted binary trees into breadth-first representation.

%C The first a(n) terms of A038774 add up to Catalan(n) = A000108(n).

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a038/A038775.java">Java program</a> (github)

%e a(5)=10 since there are 10 cycles in this permutation of forest(5), with lengths 1, 1, 3, 4, 3, 2, 16, 8, 2, 2 summing up to 42=Catalan(5).

%Y Cf. A000108, A038774.

%Y Similarly generated sequences: A001683, A002995, A003239, A057507, A057513.

%K nonn,more

%O 1,2

%A _Wouter Meeussen_, May 04 2000

%E a(13)-a(15) from _Sean A. Irvine_, May 22 2022