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 A375695 #12 Feb 06 2025 19:44:15
%S A375695 1,0,2,3,40,185,2436,20797,307616,3869217,66259900,1091351261,
%T A375695 21671302368,437191547377,9981020325836,236821065758565,
%U A375695 6144729994822336,167019469703969345,4868403452056231164,148845363155530699789,4822574537456548631360
%N A375695 Expansion of e.g.f. 1 / sqrt(1 - 2 * x * (exp(x) - 1)).
%F A375695 a(n) = n! * Sum_{k=0..floor(n/2)} A001147(k) * Stirling2(n-k,k)/(n-k)!.
%t A375695 With[{nn=20},CoefficientList[Series[1/Sqrt[1-2x (Exp[x]-1)],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Feb 06 2025 *)
%o A375695 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/sqrt(1-2*x*(exp(x)-1))))
%o A375695 (PARI) a001147(n) = prod(k=0, n-1, 2*k+1);
%o A375695 a(n) = n!*sum(k=0, n, a001147(k)*stirling(n-k, k, 2)/(n-k)!);
%Y A375695 Cf. A305404, A367880, A375687.
%K A375695 nonn
%O A375695 0,3
%A A375695 _Seiichi Manyama_, Aug 24 2024