A395386 a(n) = (2*n)! * [x^(2*n)] cosh(x) / cos(x)^3.

1, 4, 52, 1264, 48592, 2703424, 205421632, 20447497984, 2582830012672, 403755759698944, 76538801941107712, 17301582442235490304, 4598285794418840522752, 1419656731675234066776064, 503894206909911797902753792, 203768397954530049098393780224

Offset

0,2

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = 1 - (1/4) * Sum_{k=0..n-1} (-1)^(n-k) * (3 + 9^(n-k)) * binomial(2*n,2*k) * a(k).

a(n) = (1/2) * Sum_{k=0..n} binomial(2*n,2*k) * (A000364(k) + A000364(k+1)).

Prog

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

Crossrefs

Cf. A000795, A395340, A395387, A395388, A395389, A395390.

Cf. A000364.

Sequence in context: A377630 A280571 A343429 * A382676 A277353 A055974

Adjacent sequences: A395383 A395384 A395385 * A395387 A395388 A395389

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2026

Status

approved