A395292 a(n) = (2*n)! * [x^(2*n)] cos(x)^3 / cos(sqrt(2)*x).

1, -1, 5, 35, 1961, 141479, 15142253, 2233807883, 434557324241, 107785095059663, 33199576493789525, 12432680138093402483, 5562808118039117516921, 2930877575020377851090039, 1796013989349400537747402685, 1266540872143807472738548470875, 1018406407477050435716016821787041

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (-1)^n * (3 + 9^n)/4 - Sum_{k=0..n-1} (-2)^(n-k) * binomial(2*n,2*k) * a(k).

a(n) = (1/4) * Sum_{k=0..n} 2^k * (-1)^(n-k) * (3 + 9^(n-k)) * binomial(2*n,2*k) * A000364(k).

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=(-1)^i*(3+9^i)/4-sum(j=0, i-1, (-2)^(i-j)*binomial(2*i, 2*j)*v[j+1])); v;

Crossrefs

Cf. A395291, A395293, A395294.

Cf. A000364, A009117, A054879, A395296.

Sequence in context: A383521 A122590 A057991 * A000871 A263882 A035416

Adjacent sequences: A395289 A395290 A395291 * A395293 A395294 A395295

Keyword

sign

Author

Seiichi Manyama, Apr 18 2026

Status

approved