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 A352643 #18 Feb 18 2025 08:57:04
%S A352643 1,3,9,18,-27,-552,-3051,-3504,102825,1043712,3192129,-41548416,
%T A352643 -653192883,-3033406464,31367500173,670266381312,3916411302609,
%U A352643 -40460110970880,-1038593550985479,-6810646726410240,82445831323038261,2280185182260854784,15300402721484153733
%N A352643 Expansion of e.g.f. exp(3 * x * cos(x)).
%H A352643 Seiichi Manyama, <a href="/A352643/b352643.txt">Table of n, a(n) for n = 0..536</a>
%F A352643 a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
%F A352643 a(n) = Sum_{k=0..n} 3^k * i^(n-k) * A185951(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Feb 18 2025
%t A352643 With[{m = 22}, Range[0, m]! * CoefficientList[Series[Exp[3*x*Cos[x]], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A352643 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*x*cos(x))))
%o A352643 (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y A352643 Cf. A009189, A185951, A352642.
%K A352643 sign
%O A352643 0,2
%A A352643 _Seiichi Manyama_, Mar 25 2022