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 A188445 #24 Dec 05 2022 08:22:16
%S A188445 1,2,0,5,1,0,15,8,0,0,52,80,5,0,0,203,1088,205,1,0,0,877,19232,11301,
%T A188445 278,0,0,0,4140,424400,904580,67198,205,0,0,0,21147,11361786,
%U A188445 101173251,24537905,250735,80,0,0,0,115975,361058000,15207243828,13744869502
%N A188445 T(n,k) is the number of (n*k) X k binary arrays with nonzero rows in decreasing order and n ones in every column.
%H A188445 Andrew Howroyd, <a href="/A188445/b188445.txt">Table of n, a(n) for n = 1..181</a> (terms 1..69 from R. H. Hardin)
%F A188445 A(n,k) = 0 for n > 2^(k-1). - _Andrew Howroyd_, Jan 24 2020
%e A188445 Array begins:
%e A188445 ============================================================================
%e A188445 n\k| 1 2 3 4 5 6 7 8 9
%e A188445 ---+------------------------------------------------------------------------
%e A188445 1 | 1 2 5 15 52 203 877 4140 21147
%e A188445 2 | 0 1 8 80 1088 19232 424400 11361786 361058000
%e A188445 3 | 0 0 5 205 11301 904580 101173251 15207243828 2975725761202
%e A188445 4 | 0 0 1 278 67198 24537905 13744869502 11385203921707 ...
%e A188445 5 | 0 0 0 205 250735 425677958 1184910460297 ...
%e A188445 6 | 0 0 0 80 621348 5064948309 ...
%e A188445 7 | 0 0 0 15 1058139 ...
%e A188445 8 | 0 0 0 1 ...
%e A188445 ...
%e A188445 Some solutions for 16 X 4:
%e A188445 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 1 1
%e A188445 1 0 1 1 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0
%e A188445 1 0 1 0 1 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1
%e A188445 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0
%e A188445 0 1 1 1 0 1 1 0 0 1 1 1 0 1 1 0 0 1 1 1
%e A188445 0 1 0 1 0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0
%e A188445 0 1 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%e A188445 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
%o A188445 (PARI)
%o A188445 WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
%o A188445 D(p, n, k)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); WeighT(v)[n]^k/prod(i=1, #v, i^v[i]*v[i]!)}
%o A188445 T(n, k)={my(m=n*k+1, q=Vec(exp(intformal(O(x^m) - x^n/(1-x)))/(1+x))); if(n==0, 1, (-1)^m*sum(j=0, m, my(s=0); forpart(p=j, s+=(-1)^#p*D(p, n, k), [1, n]); s*q[#q-j])/2)} \\ _Andrew Howroyd_, Dec 16 2018
%Y A188445 Rows 1..5 are A000110, A002718, A060486, A188446, A188447.
%Y A188445 Columns 5..6 are A331127, A331129.
%Y A188445 Column sums are A319190.
%Y A188445 Cf. A059443, A060487, A188392, A219585, A318361, A330942, A330964, A331039.
%K A188445 nonn,tabl
%O A188445 1,2
%A A188445 _R. H. Hardin_, Mar 31 2011