A395205 - OEIS

%I #10 Apr 16 2026 09:59:00

%S 1,27,2565,540855,202178025,117975193875,99088046182125,

%T 113251719048843375,169041201902760812625,319306111422259963876875,

%U 744579461172529120356343125,2100786842974911868459722414375,7053695026382002850341408058765625,27794924948726445029416864533362671875

%N a(n) = (2*n)! * [x^(2*n)] (f(x)^3 + f(-x)^3)/2 and f(x) = 1/sqrt(1 + 2*sqrt(2)*x + x^2).

%F Let A(n,k) = (2*n)! * [x^(2*n)] (f(x)^k + f(-x)^k)/2. A(0,k) = 1 and A(n,k) = k*(k+2) * A(n-1,k+4) + k*(k+1) * A(n-1,k+2) for n > 0. a(n) = A(n,3).

%o (PARI) a(n, k=3) = if(n==0, 1, k*(k+2)*a(n-1, k+4)+k*(k+1)*a(n-1, k+2));

%Y Column k=3 of A395201.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 15 2026