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 A352642 #19 Feb 18 2025 08:57:08
%S A352642 1,2,4,2,-32,-198,-416,2634,30720,107378,-605696,-10282094,-46020608,
%T A352642 304968874,6121832448,29994597338,-279697555456,-5729595393310,
%U A352642 -26849178681344,401845799334690,7714801999937536,29062583111892506,-812705956979802112
%N A352642 Expansion of e.g.f. exp(2 * x * cos(x)).
%H A352642 Seiichi Manyama, <a href="/A352642/b352642.txt">Table of n, a(n) for n = 0..545</a>
%F A352642 a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
%F A352642 a(n) = Sum_{k=0..n} 2^k * i^(n-k) * A185951(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Feb 18 2025
%t A352642 With[{m = 22}, Range[0, m]! * CoefficientList[Series[Exp[2*x*Cos[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A352642 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*x*cos(x))))
%o A352642 (PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y A352642 Cf. A009189, A185951, A352643.
%K A352642 sign
%O A352642 0,2
%A A352642 _Seiichi Manyama_, Mar 25 2022