A395205 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).

1, 27, 2565, 540855, 202178025, 117975193875, 99088046182125, 113251719048843375, 169041201902760812625, 319306111422259963876875, 744579461172529120356343125, 2100786842974911868459722414375, 7053695026382002850341408058765625, 27794924948726445029416864533362671875

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,3).

Prog

(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));

Crossrefs

Column k=3 of A395201.

Sequence in context: A373448 A287228 A086206 * A323314 A395086 A295022

Adjacent sequences: A395202 A395203 A395204 * A395206 A395207 A395208

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2026

Status

approved