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 A300122 #7 May 24 2018 16:04:54
%S A300122 1,4,13,51,183,771,3087,13601,59933,278797,1311719,6453606,32179898,
%T A300122 166075956,871713213,4704669005,25831172649,145260890323
%N A300122 Number of normal generalized Young tableaux of size n with all rows and columns weakly increasing and all regions connected skew partitions.
%C A300122 The diagram of a connected skew partition is required to be connected as a polyomino but can have empty rows or columns. A generalized Young tableau of shape y is an array obtained by replacing the dots in the Ferrers diagram of y with positive integers. A tableau is normal if its entries span an initial interval of positive integers.
%e A300122 The a(3) = 13 tableaux:
%e A300122 1 1 1 1 1 2 1 2 2 1 2 3
%e A300122 .
%e A300122 1 1 1 1 1 2 1 2 1 3
%e A300122 1 2 1 3 2
%e A300122 .
%e A300122 1 1 1 1
%e A300122 1 1 2 2
%e A300122 1 2 2 3
%t A300122 undcon[y_]:=Select[Tuples[Range[0,#]&/@y],Function[v,GreaterEqual@@v&&With[{r=Select[Range[Length[y]],y[[#]]=!=v[[#]]&]},Or[Length[r]<=1,And@@Table[v[[i]]<y[[i+1]],{i,Range[Min@@r,Max@@r-1]}]]]]];
%t A300122 cos[y_]:=cos[y]=With[{samples=Most[undcon[y]]},If[Length[samples]===0,If[Total[y]===0,{{}},{}],Join@@Table[Prepend[#,y]&/@cos[samples[[k]]],{k,1,Length[samples]}]]];
%t A300122 Table[Sum[Length[cos[y]],{y,IntegerPartitions[n]}],{n,12}]
%Y A300122 Cf. A000085, A000898, A006958, A138178, A238690, A259479, A259480, A296561, A297388, A299699, A299925, A299926, A300118, A300120, A300121, A300123, A300124.
%K A300122 nonn,more
%O A300122 1,2
%A A300122 _Gus Wiseman_, Feb 25 2018