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 A380158 #9 Jan 14 2025 01:49:12
%S A380158 1,0,2,-4,-4,64,-8,-3312,14352,267776,-3403744,-24119360,881205184,
%T A380158 -593040384,-261913919616,2567414468864,83291021050112,
%U A380158 -2080429273726976,-22004502593928704,1526354137528335360,-3870482611349750784,-1112746657730132623360,18568218633016319670272
%N A380158 Expansion of e.g.f. sqrt(exp(-2*x) + 2*x).
%F A380158 a(n) = n! * Sum_{k=0..n} 2^k * (2*k-1)^(n-k) * binomial(1/2,k)/(n-k)!.
%F A380158 a(n) == 0 (mod 2) for n>0.
%o A380158 (PARI) a(n) = n!*sum(k=0, n, 2^k*(2*k-1)^(n-k)*binomial(1/2, k)/(n-k)!);
%Y A380158 Cf. A191498, A380014.
%K A380158 sign
%O A380158 0,3
%A A380158 _Seiichi Manyama_, Jan 13 2025