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.
a:= n-> binomial(n+1, 2)!/n!: seq(a(n), n=0..12);
g:= (n, s)-> `if`(n in s, 0, 1):
b:= proc(u, o, t, s) option remember; `if`(u+o=0, g(t, s),
`if`(g(t, s)=1, add(b(u-j, o+j-1, 1, s union {t})
, j=1..u), 0)+ add(b(u+j-1, o-j, t+1, s), j=1..o))
end:
a:= n-> b(n, 0$2, {}):
seq(a(n), n=0..24);
g[n_, s_] := If[MemberQ[s, n], 0, 1];
b[u_, o_, t_, s_] := b[u, o, t, s] = If[u + o == 0, g[t, s],
If[g[t, s] == 1, Sum[b[u - j, o + j - 1, 1, s ~Union~ {t}],
{j, u}], 0] + Sum[b[u + j - 1, o - j, t + 1, s], {j, o}]];
a[n_] := b[n, 0, 0, {}];
Table[a[n], {n, 0, 24}] (* Jean-François Alcover, Sep 01 2021, after Alois P. Heinz *)
g:= (n, s)-> `if`(n in s, 1, 0):
b:= proc(u, o, t, s) option remember; `if`(u+o=0, g(t, s),
`if`(g(t, s)=1, add(b(u-j, o+j-1, 1, s minus {t})
, j=1..u), 0)+ add(b(u+j-1, o-j, t+1, s), j=1..o))
end:
a:= n-> b(n*(n+1)/2, 0$2, {$0..n}):
seq(a(n), n=0..10);
g[n_, s_] := If[MemberQ[s, n], 1, 0];
b[u_, o_, t_, s_] := b[u, o, t, s] = If[u + o == 0, g[t, s],
If[g[t, s] == 1, Sum[b[u - j, o + j - 1, 1, s ~Complement~ {t}],
{j, u}], 0] + Sum[b[u + j - 1, o - j, t + 1, s], {j, o}]];
a[n_] := b[n(n+1)/2, 0, 0, Range[0, n]];
Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Sep 01 2021, after Alois P. Heinz *)