A395206 a(n) = (2*n)! * [x^(2*n)] (f(x)^4 + f(-x)^4)/2 and f(x) = 1/sqrt(1 + 2*sqrt(2)*x + x^2).

1, 44, 5448, 1368000, 582099840, 376473484800, 344363351270400, 423339874346188800, 673376579943395328000, 1345784983980056395776000, 3301392542765404011724800000, 9753450102655318719886786560000, 34158406495145697860977486725120000, 139935446125707791138289350344704000000

Offset

0,2

Links

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

Formula

a(n) = (2*n)! * [x^(2*n)] (1 + 10*x^2 + x^4)/(1 - 6*x^2 + x^4)^2.

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,4).

Prog

(PARI) a(n) = my(x='x+O('x^(2*n+1))); (2*n)!*polcoef((1+10*x^2+x^4)/(1-6*x^2+x^4)^2, 2*n);

Crossrefs

Column k=4 of A395201.

Sequence in context: A332562 A078279 A268548 * A203974 A390726 A266853

Adjacent sequences: A395203 A395204 A395205 * A395207 A395208 A395209

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2026

Status

approved