A395292 - OEIS

%I #17 Apr 20 2026 09:22:08

%S 1,-1,5,35,1961,141479,15142253,2233807883,434557324241,

%T 107785095059663,33199576493789525,12432680138093402483,

%U 5562808118039117516921,2930877575020377851090039,1796013989349400537747402685,1266540872143807472738548470875,1018406407477050435716016821787041

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

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

%F a(n) = (1/4) * Sum_{k=0..n} 2^k * (-1)^(n-k) * (3 + 9^(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*(3+9^i)/4-sum(j=0, i-1, (-2)^(i-j)*binomial(2*i, 2*j)*v[j+1])); v;

%Y Cf. A395291, A395293, A395294.

%Y Cf. A000364, A009117, A054879, A395296.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 18 2026