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 A136406 #9 Oct 23 2019 16:28:05
%S A136406 1,1,1,1,1,1,1,3,1,1,1,2,3,1,1,1,3,4,3,1,1,1,3,5,4,3,1,1,1,5,6,8,4,3,
%T A136406 1,1,1,4,10,8,8,4,3,1,1,1,5,10,14,11,8,4,3,1,1,1,5,12,16,17,11,8,4,3,
%U A136406 1,1,1,7,14,23,21,21,11,8,4,3,1,1,1,6,17,25,32,24,21,11,8,4,3,1,1
%N A136406 Triangle read by rows: T(n,k) is the number of bi-partitions of the pair (n,k) into pairs (n_i,k_i) of positive integers such that sum k_i = k and sum n_i*k_i^2 = n.
%C A136406 T(n,1) = T(n,n) = 1.
%C A136406 T(n,n-k) does not depend on k if k <= floor(n/2).
%H A136406 Andrew Howroyd, <a href="/A136406/b136406.txt">Table of n, a(n) for n = 1..1275</a>
%e A136406 Triangle begins:
%e A136406 1,
%e A136406 1, 1;
%e A136406 1, 1, 1;
%e A136406 1, 3, 1, 1;
%e A136406 1, 2, 3, 1, 1;
%e A136406 1, 3, 4, 3, 1, 1;
%e A136406 1, 3, 5, 4, 3, 1, 1;
%e A136406 1, 5, 6, 8, 4, 3, 1, 1;
%e A136406 1, 4, 10, 8, 8, 4, 3, 1, 1;
%e A136406 1, 5, 10, 14, 11, 8, 4, 3, 1, 1;
%e A136406 1, 5, 12, 16, 17, 11, 8, 4, 3, 1, 1;
%e A136406 ...
%o A136406 (PARI)
%o A136406 P(k, w, n)={prod(i=1, k, 1 - x^(i*w) + O(x*x^(n-k*w)))}
%o A136406 T(n)={Vecrev(polcoef(prod(w=1, sqrtint(n), sum(k=0, n\w^2, (x^w*y)^(k*w) / P(k,w^2,n))), n)/y)}
%o A136406 { for(n=1, 10, print(T(n))) } \\ _Andrew Howroyd_, Oct 23 2019
%Y A136406 Row sums are A004101.
%Y A136406 Cf. A136405, A137504.
%K A136406 nonn,tabl
%O A136406 1,8
%A A136406 _Benoit Jubin_, Apr 13 2008
%E A136406 Terms a(68) and beyond from _Andrew Howroyd_, Oct 22 2019