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 A301343 #5 Mar 19 2018 22:06:15
%S A301343 1,1,0,1,1,0,1,1,1,0,1,2,1,1,0,1,2,1,1,1,0,1,3,2,2,1,1,0,1,3,2,2,1,1,
%T A301343 1,0,1,4,2,4,1,2,1,1,0,1,4,3,4,1,3,1,1,1,0,1,5,3,6,2,4,1,2,1,1,0,1,5,
%U A301343 3,6,2,4,1,2,1,1,1,0,1,6,4,9,2,7,1,4,2,2,1,1,0
%N A301343 Regular triangle where T(n,k) is the number of planted achiral (or generalized Bethe) trees with n nodes and k leaves.
%F A301343 T(n,1) = 1, T(n,k) = 0 if n <= k, otherwise T(n,k) = Sum_{d|k} T(n - k, d).
%e A301343 Triangle begins:
%e A301343 1
%e A301343 1 0
%e A301343 1 1 0
%e A301343 1 1 1 0
%e A301343 1 2 1 1 0
%e A301343 1 2 1 1 1 0
%e A301343 1 3 2 2 1 1 0
%e A301343 1 3 2 2 1 1 1 0
%e A301343 1 4 2 4 1 2 1 1 0
%e A301343 1 4 3 4 1 3 1 1 1 0
%e A301343 1 5 3 6 2 4 1 2 1 1 0
%e A301343 The T(9,4) = 4 planted achiral trees: (((((oooo))))), ((((oo)(oo)))), (((oo))((oo))), ((o)(o)(o)(o)).
%t A301343 tri[n_,k_]:=If[k===1,1,If[k>=n,0,Sum[tri[n-k,d],{d,Divisors[k]}]]];
%t A301343 Table[tri[n,k],{n,10},{k,n}]
%Y A301343 Row sums are A003238. A version without the zeroes or first row is A214575.
%Y A301343 Cf. A000081, A003238, A004111, A032305, A055277, A214577, A273873, A289078, A289079, A290689, A291443, A298422, A298426, A301342, A301344, A301345.
%K A301343 nonn,tabl
%O A301343 1,12
%A A301343 _Gus Wiseman_, Mar 19 2018