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 A352640 #15 Feb 18 2025 08:56:47
%S A352640 1,3,9,24,45,-24,-747,-3864,-7623,48576,548001,2175360,-5269275,
%T A352640 -133496448,-785549331,789324288,52523738865,398157422592,
%U A352640 -157735851975,-31426593116160,-278010988509411,108354846277632,27060485795905221,257882404940021760
%N A352640 Expansion of e.g.f. exp(3*sin(x)).
%F A352640 a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n-1,2*k) * a(n-2*k-1).
%F A352640 a(n) = Sum_{k=0..n} 3^k * i^(n-k) * A136630(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Feb 18 2025
%t A352640 With[{m = 23}, Range[0, m]! * CoefficientList[Series[Exp[3*Sin[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A352640 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*sin(x))))
%o A352640 (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y A352640 Cf. A002017, A136630, A352639.
%Y A352640 Cf. A352280, A352638.
%K A352640 sign
%O A352640 0,2
%A A352640 _Seiichi Manyama_, Mar 25 2022