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 A352647 #23 Jun 25 2025 06:28:06
%S A352647 1,3,18,153,1728,24315,410400,8079729,181786752,4601232243,
%T A352647 129402385920,4003157532297,135098815002624,4939266681129963,
%U A352647 194472450526169088,8203835046344538465,369151362125290045440,17649035213360472293091,893431062200523039178752
%N A352647 Expansion of e.g.f. 1/(1 - 3 * x * cos(x)).
%H A352647 Seiichi Manyama, <a href="/A352647/b352647.txt">Table of n, a(n) for n = 0..384</a>
%F A352647 a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * binomial(n,2*k+1) * a(n-2*k-1).
%F A352647 a(n) = Sum_{k=0..n} 3^k * k! * i^(n-k) * A185951(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Jun 25 2025
%t A352647 With[{m = 18}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*x*Cos[x]), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A352647 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*cos(x))))
%o A352647 (PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n, 2*k+1)*a(n-2*k-1)));
%Y A352647 Cf. A352252, A352646.
%Y A352647 Cf. A352643, A352649.
%Y A352647 Cf. A185951.
%K A352647 nonn
%O A352647 0,2
%A A352647 _Seiichi Manyama_, Mar 25 2022