A395203 - OEIS

%I #10 Apr 16 2026 09:59:07

%S 1,5,249,35685,10111185,4751389125,3340612823625,3283368780817125,

%T 4298811797910254625,7231878476757166357125,

%U 15201052166635861806905625,39039802931404520330113153125,120286952837956153039829414000625,437924965690153644843300930097453125

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

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

%Y Column k=1 of A395201.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 15 2026