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 A057970 #11 Jul 14 2022 21:45:02 %S A057970 1,8,54,333,1896,9874,47164,207112,840323,3168506,11170331,37034409, %T A057970 116095018,345785753,982835676,2676217504,7005306389,17681946594, %U A057970 43153532167,102080966243,234565062960,524594120393,1143910860870 %N A057970 5 x n binary matrices with 1 unit column up to row and column permutations. %C A057970 A unit column of a binary matrix is a column with only one 1. First differences of a(n) give number of minimal 5 - covers of an unlabeled n - set that cover 6 points of that set uniquely (if offset is 6). %H A057970 Vladeta Jovovic, <a href="/A056885/a056885.pdf">Number of minimal covers of an unlabeled n - set that cover k points of that set uniquely</a> %H A057970 Vladeta Jovovic, <a href="/A057972/a057972.pdf">Number of binary matrices with fixed number of unit columns up to row and column permutations</a> %F A057970 Number of 5 x n binary matrices with k unit columns up to row and column permutations is coefficient of x^k in (1/5!)*(Z(S_n; 27 + 5*x, 27 + 5*x^2, ...) + 10*Z(S_n; 13 + 3*x, 27 + 5*x^2, 13 + 3*x^3, 27 + 5*x^4, ...) + 15*Z(S_n; 7 + x, 27 + 5*x^2, 7 + x^3, 27 + 5*x^4, ...) + 20*Z(S_n; 6 + 2*x, 6 + 2*x^2, 27 + 5*x^3, 6 + 2*x^4, 6 + 2*x^5, 27 + 5*x^6, ...) + 20*Z(S_n; 4, 6 + 2*x^2, 13 + 3*x^3, 6 + 2*x^4, 4, 27 + 5*x^6, 4, 6 + 2*x^8, 13 + 3*x^9, 6 + 2*x^10, 4, 27 + 5*x^12, ...) + 30*Z(S_n; 3 + x, 7 + x^2, 3 + x^3, 27 + 5*x^4, 3 + x^5, 7 + x^6, 3 + x^7, 27 + 5*x^8, ...) + 24*Z(S_n; 2, 2, 2, 2, 27 + 5*x^5, 2, 2, 2, 2, 27 + 5*x^10, ...)), where Z(S_n; x_1, x_2, ..., x_n) is cycle index of symmetric group S_n of degree n. %F A057970 G.f.: x/120*(5/(1 - x^1)^27 + 30/(1 - x^1)^13/(1 - x^2)^7 + 15/(1 - x^1)^7/(1 - x^2)^10 + 40/(1 - x^1)^6/(1 - x^3)^7 + 30/(1 - x^1)^3/(1 - x^2)^2/(1 - x^4)^5). %Y A057970 Cf. A001752, A056885, A057222, A057223, A057524, A057669, A057963 - A057968, A057970 - A057972, A057969, A057971, A057972. %K A057970 nonn %O A057970 1,2 %A A057970 _Vladeta Jovovic_, Oct 21 2000