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 A369723 #13 Jan 30 2024 08:23:52
%S A369723 1,4,24,208,2464,37824,720256,16450816,439245312,13440572416,
%T A369723 464007387136,17847329869824,757011972726784,35108108023349248,
%U A369723 1767517592731090944,96007679735852498944,5596725706163142393856,348533116657888468402176
%N A369723 Expansion of e.g.f. exp( 2 * (1-sqrt(1-4*x)) ).
%F A369723 a(0) = 1; a(n) = Sum_{k=0..n-1} 4^(n-k) * (n-1+k)! / (k! * (n-1-k)!).
%F A369723 a(n) = 2*(2*n-3)*a(n-1) + 16*a(n-2).
%o A369723 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*(1-sqrt(1-4*x)))))
%Y A369723 Cf. A001517, A101682, A243953, A369722, A369724.
%Y A369723 Cf. A000108.
%K A369723 nonn
%O A369723 0,2
%A A369723 _Seiichi Manyama_, Jan 30 2024