A395203 a(n) = (2*n)! * [x^(2*n)] (f(x) + f(-x))/2 and f(x) = 1/sqrt(1 + 2*sqrt(2)*x + x^2).

1, 5, 249, 35685, 10111185, 4751389125, 3340612823625, 3283368780817125, 4298811797910254625, 7231878476757166357125, 15201052166635861806905625, 39039802931404520330113153125, 120286952837956153039829414000625, 437924965690153644843300930097453125

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

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).

Prog

(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));

Crossrefs

Column k=1 of A395201.

Sequence in context: A068727 A135095 A219872 * A282734 A115739 A142202

Adjacent sequences: A395200 A395201 A395202 * A395204 A395205 A395206

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2026

Status

approved