A395289 - OEIS

%I #10 Apr 19 2026 06:08:56

%S 1,547,1560473,10951230667,143197392621233,3008649976374271987,

%T 92710641264562564107593,3938980604623358524013380507,

%U 220687547812422836917500651379553,15764564819948344309471420859821580227,1398454409757517775020864823322035690277113

%N a(n) = (2*n)! * [x^(2*n)] cos(2*x) * cos(3*x) * cos(4*x) / cos(24*x).

%F a(n) = (-1)^n * (1 + 9^n + 25^n + 81^n)/4 - Sum_{k=0..n-1} (-576)^(n-k) * binomial(2*n,2*k) * a(k).

%o (PARI) a_vector(n, s=2, t=3, u=4) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i*((s+t+u)^(2*i)+(s+t-u)^(2*i)+(s-t+u)^(2*i)+(s-t-u)^(2*i))/4-sum(j=0, i-1, (-(s*t*u)^2)^(i-j)*binomial(2*i, 2*j)*v[j+1])); v;

%Y Cf. A395290.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 18 2026