A352647 - OEIS

%I #18 Mar 27 2022 02:15:03

%S 1,3,18,153,1728,24315,410400,8079729,181786752,4601232243,

%T 129402385920,4003157532297,135098815002624,4939266681129963,

%U 194472450526169088,8203835046344538465,369151362125290045440,17649035213360472293091,893431062200523039178752

%N Expansion of e.g.f. 1/(1 - 3 * x * cos(x)).

%H Seiichi Manyama, <a href="/A352647/b352647.txt">Table of n, a(n) for n = 0..384</a>

%F 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).

%t With[{m = 18}, Range[0, m]! * CoefficientList[Series[1/(1 - 3*x*Cos[x]), {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1-3*x*cos(x))))

%o (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 Cf. A352252, A352646.

%Y Cf. A352643, A352649.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 25 2022