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 A357663 #13 Aug 13 2025 18:12:56
%S A357663 1,0,4,48,464,4480,48448,621824,9320704,154890240,2746131456,
%T A357663 51237908480,1007228375040,20965557829632,463091379159040,
%U A357663 10826828061147136,266438312153120768,6861616219559034880,184128217520198123520,5135753969867535941632
%N A357663 Expansion of e.g.f. cosh( (exp(4*x) - 1)/2 ).
%F A357663 a(n) = Sum_{k=0..floor(n/2)} 4^(n-k) * Stirling2(n,2*k).
%t A357663 With[{nn=20},CoefficientList[Series[Cosh[(Exp[4x]-1)/2],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 13 2025 *)
%o A357663 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(cosh((exp(4*x)-1)/2)))
%o A357663 (PARI) a(n) = sum(k=0, n\2, 4^(n-k)*stirling(n, 2*k, 2));
%Y A357663 Cf. A024430, A357661, A357662.
%Y A357663 Cf. A065143, A357650, A357666.
%K A357663 nonn
%O A357663 0,3
%A A357663 _Seiichi Manyama_, Oct 07 2022