A395291 a(n) = (2*n)! * [x^(2*n)] cos(x)^2 / cos(sqrt(2)*x).

1, 0, 4, 96, 4368, 318720, 34102336, 5030914560, 978697675008, 242750559363072, 74771153253336064, 28000532879379456000, 12528400144123416219648, 6600840125120447062671360, 4044932243925079634651398144, 2852467766044703580371025002496, 2293626296595266305722457178308608

Offset

0,3

Links

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

Formula

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

a(n) = (1/2) * Sum_{k=0..n} 2^k * (-1)^(n-k) * (0^(n-k) + 4^(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*(0^i+4^i)/2-sum(j=0, i-1, (-2)^(i-j)*binomial(2*i, 2*j)*v[j+1])); v;

Crossrefs

Cf. A371684, A395292, A395293, A395294.

Cf. A000364, A009117, A394478.

Sequence in context: A221148 A317664 A062779 * A077155 A013042 A190196

Adjacent sequences: A395288 A395289 A395290 * A395292 A395293 A395294

Keyword

nonn

Author

Seiichi Manyama, Apr 18 2026

Status

approved