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 A360873 #13 Feb 16 2025 08:34:04
%S A360873 1,3,3,7,13,7,15,51,51,15,31,205,397,205,31,63,843,3303,3303,843,63,
%T A360873 127,3493,27877,55933,27877,3493,127,255,14451,233751,943095,943095,
%U A360873 233751,14451,255,511,59485,1938517,15678925,31450861,15678925,1938517,59485,511
%N A360873 Array read by antidiagonals: T(m,n) is the number of (non-null) connected induced subgraphs in the rook graph K_m X K_n.
%H A360873 Andrew Howroyd, <a href="/A360873/b360873.txt">Table of n, a(n) for n = 1..1275</a> (first 50 antidiagonals).
%H A360873 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>.
%H A360873 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Vertex-InducedSubgraph.html">Vertex-Induced Subgraph</a>.
%F A360873 T(m,n) = Sum_{i=1..m} Sum_{j=1..n} binomial(m, i) * binomial(n, j) * A262307(i, j).
%F A360873 T(m,n) = T(n,m).
%e A360873 Array begins:
%e A360873 =======================================================
%e A360873 m\n| 1 2 3 4 5 6 ...
%e A360873 ---+---------------------------------------------------
%e A360873 1 | 1 3 7 15 31 63 ...
%e A360873 2 | 3 13 51 205 843 3493 ...
%e A360873 3 | 7 51 397 3303 27877 233751 ...
%e A360873 4 | 15 205 3303 55933 943095 15678925 ...
%e A360873 5 | 31 843 27877 943095 31450861 1033355223 ...
%e A360873 6 | 63 3493 233751 15678925 1033355223 67253507293 ...
%e A360873 ...
%o A360873 (PARI) \\ S is A183109, T is A262307, U is this sequence.
%o A360873 G(M,N=M)={ my(S=matrix(M, N), T=matrix(M, N), U=matrix(M, N));
%o A360873 for(m=1, M, for(n=1, N,
%o A360873 S[m, n]=sum(j=0, m, (-1)^j*binomial(m, j)*(2^(m - j) - 1)^n);
%o A360873 T[m, n]=S[m, n]-sum(i=1, m-1, sum(j=1, n-1, T[i, j]*S[m-i, n-j]*binomial(m-1, i-1)*binomial(n, j)));
%o A360873 U[m, n]=sum(i=1, m, sum(j=1, n, binomial(m, i)*binomial(n, j)*T[i, j])) )); U
%o A360873 }
%o A360873 { my(A=G(7)); for(n=1, #A~, print(A[n,])) }
%Y A360873 Main diagonal is A286189.
%Y A360873 Rows 1..2 are A000225, A360874.
%Y A360873 Cf. A360850, A360851, A360853, A360875.
%K A360873 nonn,tabl
%O A360873 1,2
%A A360873 _Andrew Howroyd_, Feb 24 2023