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 A358607 #17 Jun 14 2024 11:53:17
%S A358607 1,1,1,5,23,115,697,4925,39623,357955,3589177,39558845,475412423,
%T A358607 6187461955,86702878777,1301486906045,20836087009223,354385941189955,
%U A358607 6381537618718777,121290714467642045,2426520470557921223,50969651457241797955,1121574207307049758777
%N A358607 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * (n-2*k)!.
%H A358607 Seiichi Manyama, <a href="/A358607/b358607.txt">Table of n, a(n) for n = 0..449</a>
%F A358607 a(n) = n * a(n-1) - a(n-2) + n * a(n-3) for n > 2.
%F A358607 a(n) ~ n! * (1 - 1/n^2 - 1/n^3 + 5/n^5 + 23/n^6 + 74/n^7 + 161/n^8 - 57/n^9 - 3466/n^10 - ...), for coefficients see A121868. - _Vaclav Kotesovec_, Nov 25 2022
%F A358607 a(2n) = 1+A215096(2n). a(2n+1) = A215096(2n+1). - _R. J. Mathar_, Jun 14 2024
%o A358607 (PARI) a(n) = sum(k=0, n\2, (-1)^k*(n-2*k)!);
%Y A358607 Cf. A358608, A358609, A358611.
%Y A358607 Cf. A121868, A136580.
%K A358607 nonn
%O A358607 0,4
%A A358607 _Seiichi Manyama_, Nov 23 2022