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 A352639 #18 Feb 18 2025 09:00:29
%S A352639 1,2,4,6,0,-46,-192,-266,1792,14114,34816,-171930,-2027520,-6522382,
%T A352639 34750464,496296022,1748500480,-12731696062,-186550845440,
%U A352639 -617309234490,7292215885824,99199654760978,248883934396416,-5836506132182090,-69729013345550336
%N A352639 Expansion of e.g.f. exp(2*sin(x)).
%F A352639 a(0) = 1; a(n) = 2 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1).
%F A352639 a(n) = Sum_{k=0..n} 2^k * i^(n-k) * A136630(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Feb 18 2025
%t A352639 With[{m = 24}, Range[0, m]! * CoefficientList[Series[Exp[2*Sin[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A352639 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(2*sin(x))))
%o A352639 (PARI) a(n) = if(n==0, 1, 2*sum(k=0, (n-1)\2, (-1)^k*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y A352639 Cf. A002017, A136630, A352640.
%Y A352639 Cf. A007289, A352279, A352642.
%K A352639 sign
%O A352639 0,2
%A A352639 _Seiichi Manyama_, Mar 25 2022