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 A356630 #14 Aug 19 2022 09:25:16
%S A356630 1,1,1,1,1,121,721,2521,6721,378001,7287841,59930641,319429441,
%T A356630 7524471241,353072319601,5897248517161,55827317669761,726274560953761,
%U A356630 53139878190826561,1650487849152976801,25981849479032542081,317292238756098973081
%N A356630 a(n) = n! * Sum_{k=0..floor(n/4)} (n - 4*k)^k/(n - 4*k)!.
%F A356630 E.g.f.: Sum_{k>=0} x^k / (k! * (1 - k*x^4)).
%t A356630 a[n_] := n! * Sum[(n - 4*k)^k/(n - 4*k)!, {k, 0, Floor[n/4]}]; a[0] = 1; Array[a, 22, 0] (* _Amiram Eldar_, Aug 19 2022 *)
%o A356630 (PARI) a(n) = n!*sum(k=0, n\4, (n-4*k)^k/(n-4*k)!);
%o A356630 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, x^k/(k!*(1-k*x^4)))))
%Y A356630 Cf. A354436, A356628, A356629.
%Y A356630 Cf. A354554, A356634.
%K A356630 nonn
%O A356630 0,6
%A A356630 _Seiichi Manyama_, Aug 18 2022