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 A302396 #23 Jan 16 2024 22:05:43
%S A302396 1,0,0,0,1,26,32596,34359509614,1180591620442534312297,
%T A302396 85070591730234605240519066638188154620,
%U A302396 1645504557321206042154968331851433202636630333819989444275003856
%N A302396 Number of families of 4-subsets of an n-set that cover every element.
%C A302396 Number of simple 4-uniform hypergraphs of order n without isolated vertices.
%H A302396 Andrew Howroyd, <a href="/A302396/b302396.txt">Table of n, a(n) for n = 0..18</a>
%F A302396 a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k) * 2^binomial(n-k,4).
%e A302396 For n=5 all families with at least two 4-sets will cover every element.
%p A302396 seq(add((-1)^k * binomial(n,k) * 2^binomial(n-k,4), k = 0..n), n=0..12)
%t A302396 Array[Sum[(-1)^k*Binomial[#, k] 2^Binomial[# - k, 4], {k, 0, #}] &, 11, 0] (* _Michael De Vlieger_, Apr 07 2018 *)
%o A302396 (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n,k)*2^binomial(n-k,4)); \\ _Michel Marcus_, Apr 07 2018
%o A302396 (GAP) Flat(List([0..10],n->Sum([0..n],k->(-1)^k*Binomial(n,k)*2^Binomial(n-k,4)))); # _Muniru A Asiru_, Apr 07 2018
%Y A302396 Column 4 of A299471.
%Y A302396 Cf. A302394.
%K A302396 nonn,easy
%O A302396 0,6
%A A302396 _Brendan McKay_, Apr 07 2018