A395389 a(n) = (2*n)! * [x^(2*n)] cosh(x) / cos(x)^6.

1, 7, 157, 6307, 381817, 31966207, 3511363477, 488071502107, 83574391985137, 17266040350902007, 4232061273781286797, 1213740765474529653907, 402564619773368808708457, 152873186645617612638445807, 65893166000017900760491690117, 31993048699386236951110199165707

Offset

0,2

Links

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

Formula

a(n) = 1 - (1/32) * Sum_{k=0..n-1} (-1)^(n-k) * (15*4^(n-k) + 6*16^(n-k) + 36^(n-k)) * binomial(2*n,2*k) * a(k).

a(n) = (1/120) * Sum_{k=0..n} binomial(2*n,2*k) * (64*A000182(k+1) + 20*A000182(k+2) + A000182(k+3)).

Prog

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

Crossrefs

Cf. A000795, A395340, A395386, A395387, A395388, A395390.

Cf. A000182, A385343, A395384.

Sequence in context: A073605 A115866 A197766 * A009703 A014385 A114485

Adjacent sequences: A395386 A395387 A395388 * A395390 A395391 A395392

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2026

Status

approved