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 A380028 #9 Apr 22 2025 13:00:59
%S A380028 1,-1,-3,-12,-79,-760,-9561,-147994,-2716239,-57632040,-1387518625,
%T A380028 -37365406606,-1112793904311,-36312032900884,-1288357188957489,
%U A380028 -49380149141206290,-2033232328710195871,-89506187915127440560,-4194948681994077973377,-208545134727411799745878
%N A380028 Expansion of e.g.f. sqrt(1 - 2*x*exp(x)).
%F A380028 a(n) = n! * Sum_{k=0..n} (-2)^k * k^(n-k) * binomial(1/2,k)/(n-k)!.
%t A380028 With[{nn=20},CoefficientList[Series[Sqrt[1-2x Exp[x]],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Apr 22 2025 *)
%o A380028 (PARI) a(n) = n!*sum(k=0, n, (-2)^k*k^(n-k)*binomial(1/2, k)/(n-k)!);
%Y A380028 Cf. A002420, A380015.
%K A380028 sign,easy
%O A380028 0,3
%A A380028 _Seiichi Manyama_, Jan 09 2025