A395384 a(n) = (2*n)! * [x^(2*n)] 1 / cos(x)^6.

1, 6, 120, 4416, 249600, 19781376, 2078100480, 278400270336, 46222559477760, 9302629468471296, 2229557114964541440, 627125152804037984256, 204500159955172086251520, 76507021194866780553609216, 32543054888758773094023168000, 15614979509514628186072128946176

Offset

0,2

Links

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

Formula

a(0) = 1; a(n) = -(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) * (64*A000182(n+1) + 20*A000182(n+2) + A000182(n+3)).

Prog

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

Crossrefs

Cf. A000182, A326327, A385343.

Sequence in context: A029697 A248045 A280627 * A196688 A126448 A126446

Adjacent sequences: A395381 A395382 A395383 * A395385 A395386 A395387

Keyword

nonn

Author

Seiichi Manyama, Apr 20 2026

Status

approved