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 A376935 #16 May 01 2025 08:31:39
%S A376935 1,1,1,1,2,1,1,6,6,1,1,20,90,20,1,1,70,1860,1860,70,1,1,252,44730,
%T A376935 297200,44730,252,1,1,924,1172556,60871300,60871300,1172556,924,1,1,
%U A376935 3432,32496156,14367744720,116963796250,14367744720,32496156,3432,1,1,12870,936369720,3718394156400,273957842462220,273957842462220,3718394156400,936369720,12870,1
%N A376935 Array read by antidiagonals: T(n,k) is the number of 2*n X 2*k binary matrices with all row sums k and column sums n.
%C A376935 T(n,k) is the number of 2*n X 2*k {-1,1} matrices with all rows and columns summing to zero.
%H A376935 Nikolai Beluhov, <a href="https://arxiv.org/abs/2504.21451">Powers of 2 in Balanced Grid Colourings</a>, arXiv:2504.21451 [math.CO], 2025.
%H A376935 Robert Dougherty-Bliss, Christoph Koutschan, Natalya Ter-Saakov, and Doron Zeilberger, <a href="https://arxiv.org/abs/2410.07435">The (Symbolic and Numeric) Computational Challenges of Counting 0-1 Balanced Matrices</a>, arXiv:2410.07435 [math.CO], 2024.
%F A376935 T(n,k) = T(k,n).
%e A376935 Array begins:
%e A376935 ========================================================================
%e A376935 n\k | 0 1 2 3 4 5 ...
%e A376935 ----+------------------------------------------------------------------
%e A376935 0 | 1 1 1 1 1 1 ...
%e A376935 1 | 1 2 6 20 70 252 ...
%e A376935 2 | 1 6 90 1860 44730 1172556 ...
%e A376935 3 | 1 20 1860 297200 60871300 14367744720 ...
%e A376935 4 | 1 70 44730 60871300 116963796250 273957842462220 ...
%e A376935 5 | 1 252 1172556 14367744720 273957842462220 6736218287430460752 ...
%e A376935 ...
%o A376935 (PARI)
%o A376935 T(n, k)={
%o A376935 local(M=Map(Mat([2*k, 1])));
%o A376935 my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));
%o A376935 my(recurse(i, p, v, e) = if(i<0, if(!e, acc(p, v)), my(t=polcoef(p,i)); for(j=0, min(t, e), self()(i-1, p+j*(x-1)*x^i, binomial(t, j)*v, e-j))));
%o A376935 for(r=1, 2*n, my(src=Mat(M)); M=Map(); for(i=1, matsize(src)[1], recurse(n-1, src[i, 1], src[i, 2], k))); vecsum(Mat(M)[,2]);
%o A376935 }
%Y A376935 Main diagonal is A058527.
%Y A376935 Columns 0..9 are A000012, A000984, A002896, A172556, A172555, A172557, A172558, A172559, A172560, A172554.
%Y A376935 Cf. A008300, A195644, A333901, A334549, A377007 (up to permutations of rows and columns).
%K A376935 nonn,tabl
%O A376935 0,5
%A A376935 _Andrew Howroyd_, Oct 11 2024