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%I #31 May 30 2022 19:36:36
%S 1,1,1,2,1,1,2,2,1,1,4,3,2,1,1,5,4,3,2,1,1,9,6,5,3,2,1,1,13,10,6,5,3,
%T 2,1,1,23,15,10,7,5,3,2,1,1,35,24,14,10,7,5,3,2,1,1,61,39,23,14,11,7,
%U 5,3,2,1,1,98,63,34,21,14,11,7,5,3,2,1,1
%N Triangle read by rows: T(n,k), 2 <= k < n is the number of n-element k-ary unlabeled rooted trees where a subtree consisting of h + 1 nodes has exactly min{h,k} subtrees.
%e Triangle begins:
%e 1;
%e 1, 1;
%e 2, 1, 1;
%e 2, 2, 1, 1;
%e 4, 3, 2, 1, 1;
%e 5, 4, 3, 2, 1, 1;
%e 9, 6, 5, 3, 2, 1, 1;
%e 13, 10, 6, 5, 3, 2, 1, 1;
%e 23, 15, 10, 7, 5, 3, 2, 1, 1;
%e 35, 24, 14, 10, 7, 5, 3, 2, 1, 1;
%e 61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1;
%e 98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1;
%e In particular, the rooted trees counted in the first three rows of the triangle are shown by using the Hasse diagram as follows:
%e ---------
%e o o
%e \ /
%e o
%e ----------------------
%e o |
%e | |
%e o o | o o o
%e \ / | \ | /
%e o | o
%e ------------------------------------------------------
%e o o o o | o |
%e \ / | | | | |
%e o o o o | o o o | o o o o
%e \ / \ / | \ | / | \ \ / /
%e o o | o | o
%Y Cf. A000081, A000598, A001190, A292556, A299038.
%K nonn,tabl
%O 3,4
%A _Salah Uddin Mohammad_, Mar 17 2022
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