A395291 - OEIS

%I #17 Apr 20 2026 09:22:11

%S 1,0,4,96,4368,318720,34102336,5030914560,978697675008,

%T 242750559363072,74771153253336064,28000532879379456000,

%U 12528400144123416219648,6600840125120447062671360,4044932243925079634651398144,2852467766044703580371025002496,2293626296595266305722457178308608

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

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

%F 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).

%o (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;

%Y Cf. A371684, A395292, A395293, A395294.

%Y Cf. A000364, A009117, A394478.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Apr 18 2026