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 A334689 #20 May 11 2020 11:22:03 %S A334689 1,1,1,1,9,2,1,49,72,6,1,225,1250,600,24,1,961,16200,25350,5400,120,1, %T A334689 3969,181202,735000,470400,52920,720,1,16129,1866312,17360406, %U A334689 26460000,8490720,564480,5040,1,65025,18301250,362237400,1159593624,840157920,153679680,6531840,40320 %N A334689 Triangle read by rows: T(n,k) (0 <= k <= n) = k!*(Stirling2(n,k)+(k+1)*Stirling2(n,k+1))^2. %C A334689 This is the number of Boolean matrices of dimension n and rank k having a Moore-Penrose inverse (Kim-Roush, Th. 10). %C A334689 Theorem 8 of the same Kim-Roush paper gives a formula for the number of Boolean matrices of dimension n and rank k having a minimum-norm g-inverse. Unfortunately the formula appears to produce negative numbers. %H A334689 Ki Hang Kim, and Fred W. Roush, <a href="https://doi.org/10.1016/0024-3795(78)90075-7">Inverses of Boolean matrices</a>, Linear Algebra and its Applications 22 (1978): 247-262. See Th. 10. %e A334689 Triangle begins: %e A334689 1, %e A334689 1, 1, %e A334689 1, 9, 2, %e A334689 1, 49, 72, 6, %e A334689 1, 225, 1250, 600, 24, %e A334689 1, 961, 16200, 25350, 5400, 120, %e A334689 1, 3969, 181202, 735000, 470400, 52920, 720, %e A334689 1, 16129, 1866312, 17360406, 26460000, 8490720, 564480, 5040, %e A334689 ... %p A334689 T := (n,k) -> k!*(Stirling2(n,k)+(k+1)*Stirling2(n,k+1))^2; %p A334689 r:=n->[seq(T(n,k),k=0..n)]; %p A334689 for n from 0 to 12 do lprint(r(n)); od: %Y A334689 Columns k=0-2 give: A000012, A060867, 2*A129839(n+1). %Y A334689 Row sums give A014235. %K A334689 nonn,tabl %O A334689 0,5 %A A334689 _N. J. A. Sloane_, May 11 2020