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 A373027 #6 May 20 2024 10:30:15 %S A373027 1,4,32,400,6660,138576,3460464,100821904,3357239440 %N A373027 Number of (0,1)-matrices with sum of entries equal to 2*n or 2*n+1, no zero rows or columns, which are centrally symmetric. %C A373027 a(n) is the number ordered pairs of semistandard Young tableaux of size 2*n or 2*n+1 with consecutive entries (i.e., if i is in T, and 1<=j<=i, then j is in T) and with conjugate shapes, which are both invariant under Schützenberger involution. %e A373027 The a(2) = 32 matrices with sum of entries equal to 4: %e A373027 [1 0 0 0] [0 0 0 1] [1 0 0 0] [0 0 0 1] [0 0 1 0] [0 1 0 0] %e A373027 [0 1 0 0] [0 1 0 0] [0 0 1 0] [0 0 1 0] [0 0 0 1] [1 0 0 0] %e A373027 [0 0 1 0] [0 0 1 0] [0 1 0 0] [0 1 0 0] [1 0 0 0] [0 0 0 1] %e A373027 [0 0 0 1] [1 0 0 0] [0 0 0 1] [1 0 0 0] [0 1 0 0] [0 0 1 0] %e A373027 . %e A373027 [0 1 0 0] [0 0 1 0] [1 0 0] [0 1 0] [0 1 0] [0 0 1] %e A373027 [0 0 0 1] [1 0 0 0] [0 1 0] [1 0 0] [0 0 1] [0 1 0] %e A373027 [1 0 0 0] [0 0 0 1] [0 1 0] [0 0 1] [1 0 0] [0 1 0] %e A373027 [0 0 1 0] [0 1 0 0] [0 0 1] [0 1 0] [0 1 0] [1 0 0] %e A373027 . %e A373027 [1 0] [0 1] [1 0] [0 1] [1] %e A373027 [1 0] [0 1] [0 1] [1 0] [1] %e A373027 [0 1] [1 0] [1 0] [0 1] [1] %e A373027 [0 1] [1 0] [0 1] [1 0] [1] %e A373027 . %e A373027 [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] [0 1 0] [1 0] [0 1] %e A373027 [0 1 1 0] [1 0 0 1] [1 0 0 1] [0 1 1 0] [1 0 1] [1 1] [1 1] %e A373027 [0 0 0 1] [0 0 1 0] [0 1 0 0] [1 0 0 0] [0 1 0] [0 1] [1 0] %e A373027 . %e A373027 [1 1 0 0] [0 0 1 1] [1 0 1 0] [0 1 0 1] [1 1 0] [0 1 1] [1 1] %e A373027 [0 0 1 1] [1 1 0 0] [0 1 0 1] [1 0 1 0] [0 1 1] [1 1 0] [1 1] %e A373027 . %e A373027 [1 1 1 1] %Y A373027 Cf. A275787, A370396. %K A373027 nonn,more %O A373027 0,2 %A A373027 _Ludovic Schwob_, May 20 2024