A395202 a(n) = (2*n)! * [x^(2*n)] (f(x)^3 + f(-x)^3)/2 and f(x) = 1/(cosh(x) - sqrt(2) * sinh(x)).

1, 21, 849, 61941, 7214529, 1229315061, 288483011409, 89219766504981, 35169525934911489, 17212551024649711701, 10240591076060907554769, 7278858609414500847895221, 6091844983487415298481901249, 5929573147218620069431200095541, 6641729004270943179521683072030929

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = (2*n)! * [x^(2*n)] cosh(x) * (1 + 7*sinh(x)^2)/(1 - sinh(x)^2)^3.

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+1) * A(n-1,k+2) + k^2 * A(n-1,k) for n > 0. a(n) = A(n,3).

Prog

(PARI) a(n) = my(x='x+O('x^(2*n+1))); (2*n)!*polcoef(cosh(x)*(1+7*sinh(x)^2)/(1-sinh(x)^2)^3, 2*n);

Crossrefs

Column k=3 of A395200.

Sequence in context: A366301 A119414 A012819 * A297718 A296384 A296641

Adjacent sequences: A395199 A395200 A395201 * A395203 A395204 A395205

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2026

Status

approved