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.
A219274 with rows reversed begins: 1; 1; 1; 1, 2; 1, 3; 1, 4, 5; 1, 5, 9, 16; 1, 6, 14, 49; 1, 7, 20, 92, 70; 1, 8, 27, 153, 204, 168; 1, 9, 35, 235, 405, 738, 768; ...
h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
end:
g:= proc(n, i, l) local s; s:=i*(i+1)/2;
`if`(n=s, h([l[], seq(i-j, j=0..i-1)]), `if`(n>s, 0,
g(n, i-1, l)+ `if`(i>n, 0, g(n-i, i-1, [l[], i]))))
end:
T:= (n, k)-> `if`(k>n, 0, g(n-k, k-1, [k])):
seq(seq(T(n, n-k), k=0..(n-floor(sqrt(2*n)+1/2))), n=0..14);
h:= proc(l) local n; n:=nops(l); add(i, i=l)!/mul(mul(1+l[i]-j+
add(`if`(l[k]>=j, 1, 0), k=i+1..n), j=1..l[i]), i=1..n)
end:
g:= proc(n, i, l) local s; s:=ceil(i*(i+2)/4);
`if`(n=s, h([l[], seq(i-2*j, j=0..iquo(i-1,2))]), `if`(n>s, 0,
g(n, i-1, l)+`if`(i>n, 0, g(n-i, i-2, [l[], i]))))
end:
a:= n-> g(n, n, []):
seq(a(n), n=0..35); # Alois P. Heinz, Apr 29 2013
h[l_List] := Module[{n}, n = Length[l]; Total[l]!/Product[Product[1 + l[[i]] - j + Sum[If[l[[k]] >= j, 1, 0], {k, i+1, n}], {j, 1, l[[i]]}], {i, 1, n}]]; g[n_, i_, l_List] := Module[{s}, s = Ceiling[i*(i+2)/4]; If[n==s, h[Join[l, Table[i-2*j, {j, 0, Quotient[i-1, 2]}]]], If[n>s, 0, g[n, i-1, l] + If[i>n, 0, g[n-i, i-2, Append[l, i]]]]]]; a[n_] := g[n, n, {}]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jul 02 2015, after Alois P. Heinz *)
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