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%I #6 Mar 21 2021 10:16:38
%S 1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,2,0,1,0,1,0,0,3,0,1,0,1,0,5,0,3,0,1,
%T 0,1,0,0,7,0,3,0,1,0,1,0,14,0,8,0,3,0,1,0,1,0,0,22,0,8,0,3,0,1,0,1,0,
%U 42,0,24,0,8,0,3,0,1,0,1,0,0,66,0,25,0,8,0
%N T(n,k) is the number of rooted plane binary forests with n nodes and k trees: triangle read by rows.
%C Multiset transform of A126120.
%e See A222006 showing T(6,k).
%e The triangle starts (n>=0, 0<=k<=n):
%e 1
%e 0 1
%e 0 0 1
%e 0 1 0 1
%e 0 0 1 0 1
%e 0 2 0 1 0 1
%e 0 0 3 0 1 0 1
%e 0 5 0 3 0 1 0 1
%e 0 0 7 0 3 0 1 0 1
%e 0 14 0 8 0 3 0 1 0 1
%e 0 0 22 0 8 0 3 0 1 0 1
%e 0 42 0 24 0 8 0 3 0 1 0 1
%e 0 0 66 0 25 0 8 0 3 0 1 0 1
%e 0 132 0 74 0 25 0 8 0 3 0 1 0 1
%e 0 0 217 0 76 0 25 0 8 0 3 0 1 0 1
%Y Cf. A222006 (row sums), A126120 (column k=1), A007595 (k=2), A046342 (k=3), A088327 (limit n->oo, row reverse).
%K nonn,tabl
%O 0,17
%A _R. J. Mathar_, Mar 21 2021
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