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 A342770 #6 Mar 21 2021 10:16:38 %S A342770 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 A342770 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 A342770 42,0,24,0,8,0,3,0,1,0,1,0,0,66,0,25,0,8,0 %N A342770 T(n,k) is the number of rooted plane binary forests with n nodes and k trees: triangle read by rows. %C A342770 Multiset transform of A126120. %e A342770 See A222006 showing T(6,k). %e A342770 The triangle starts (n>=0, 0<=k<=n): %e A342770 1 %e A342770 0 1 %e A342770 0 0 1 %e A342770 0 1 0 1 %e A342770 0 0 1 0 1 %e A342770 0 2 0 1 0 1 %e A342770 0 0 3 0 1 0 1 %e A342770 0 5 0 3 0 1 0 1 %e A342770 0 0 7 0 3 0 1 0 1 %e A342770 0 14 0 8 0 3 0 1 0 1 %e A342770 0 0 22 0 8 0 3 0 1 0 1 %e A342770 0 42 0 24 0 8 0 3 0 1 0 1 %e A342770 0 0 66 0 25 0 8 0 3 0 1 0 1 %e A342770 0 132 0 74 0 25 0 8 0 3 0 1 0 1 %e A342770 0 0 217 0 76 0 25 0 8 0 3 0 1 0 1 %Y A342770 Cf. A222006 (row sums), A126120 (column k=1), A007595 (k=2), A046342 (k=3), A088327 (limit n->oo, row reverse). %K A342770 nonn,tabl %O A342770 0,17 %A A342770 _R. J. Mathar_, Mar 21 2021