A395289 a(n) = (2*n)! * [x^(2*n)] cos(2*x) * cos(3*x) * cos(4*x) / cos(24*x).

1, 547, 1560473, 10951230667, 143197392621233, 3008649976374271987, 92710641264562564107593, 3938980604623358524013380507, 220687547812422836917500651379553, 15764564819948344309471420859821580227, 1398454409757517775020864823322035690277113

Offset

0,2

Links

Table of n, a(n) for n=0..10.

Formula

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).

Prog

(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;

Crossrefs

Cf. A395290.

Sequence in context: A300899 A253546 A015324 * A103537 A136928 A249297

Adjacent sequences: A395286 A395287 A395288 * A395290 A395291 A395292

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2026

Status

approved