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 A214020 #31 Oct 05 2018 20:06:53
%S A214020 1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,0,2,0,1,1,1,1,2,6,6,2,
%T A214020 1,1,1,1,0,22,0,22,0,1,1,1,1,5,92,324,324,92,5,1,1,1,1,0,422,0,8716,0,
%U A214020 422,0,1,1,1,1,14,2074,47570,343234,343234,47570,2074,14,1,1
%N A214020 Number A(n,k) of n X k chess tableaux; square array A(n,k), n>=0, k>=0, read by antidiagonals.
%C A214020 A standard Young tableau (SYT) with cell(i,j)+i+j == 1 mod 2 for all cells is called a chess tableau. The definition appears first in the article by Jonas Sjöstrand.
%H A214020 Alois P. Heinz, <a href="/A214020/b214020.txt">Antidiagonals n = 0..24, flattened</a>
%H A214020 T. Y. Chow, H. Eriksson and C. K. Fan, <a href="http://www.combinatorics.org/Volume_11/Abstracts/v11i2a3.html">Chess tableaux</a>, Elect. J. Combin., 11 (2) (2005), #A3.
%H A214020 Jonas Sjöstrand, <a href="https://arxiv.org/abs/math/0309231v3">On the sign-imbalance of partition shapes</a>, arXiv:math/0309231v3 [math.CO], 2005.
%H A214020 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%e A214020 A(4,3) = A(3,4) = 6:
%e A214020 [1 4 7] [1 4 5] [1 2 3] [1 4 7] [ 1 4 7] [ 1 2 3]
%e A214020 [2 5 10] [2 7 10] [4 7 10] [2 5 10] [ 2 5 8] [ 4 5 6]
%e A214020 [3 8 11] [3 8 11] [5 8 11] [3 6 11] [ 3 6 9] [ 7 8 9]
%e A214020 [6 9 12] [6 9 12] [6 9 12] [8 9 12] [10 11 12] [10 11 12].
%e A214020 Square array A(n,k) begins:
%e A214020 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A214020 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A214020 1, 1, 0, 1, 0, 2, 0, 5, ...
%e A214020 1, 1, 1, 2, 6, 22, 92, 422, ...
%e A214020 1, 1, 0, 6, 0, 324, 0, 47570, ...
%e A214020 1, 1, 2, 22, 324, 8716, 343234, 17423496, ...
%e A214020 1, 1, 0, 92, 0, 343234, 0, 8364334408, ...
%e A214020 1, 1, 5, 422, 47570, 17423496, 8364334408, 6873642982160, ...
%p A214020 b:= proc() option remember; local s; s:= add(i, i=args); `if`(s=0, 1,
%p A214020 add(`if`(irem(s+i-args[i], 2)=1 and args[i]>`if`(i=nargs, 0,
%p A214020 args[i+1]), b(subsop(i=args[i]-1, [args])[]), 0), i=1..nargs))
%p A214020 end:
%p A214020 A:= (n, k)-> `if`(n<k, A(k, n), `if`(k<2, 1, b(n$k))):
%p A214020 seq(seq(A(n, d-n), n=0..d), d=0..12);
%t A214020 b[args_List] := b[args] = Module[{s = Total[args], nargs = Length[args]}, If[s == 0, 1, Sum[If[Mod[s + i - args[[i]], 2] == 1 && args[[i]] > If[i == nargs, 0, args[[i + 1]]], b[ReplacePart[args, i -> args[[i]] - 1]], 0], {i, 1, nargs}]]]; A[n_, k_] := If[n < k, A[k, n], If[k < 2, 1, b[Array[n &, k]]]]; Table[Table[A[n, d - n], {n, 0, d}], {d, 0, 12}] // Flatten (* _Jean-François Alcover_, Jan 21 2015, after _Alois P. Heinz_ *)
%Y A214020 Cf. A000108 (bisection of row 2), A001181 (row 3), A108774, A214021, A214088.
%K A214020 nonn,tabl
%O A214020 0,25
%A A214020 _Alois P. Heinz_, Jul 01 2012