A395384 - OEIS

%I #8 Apr 21 2026 09:06:22

%S 1,6,120,4416,249600,19781376,2078100480,278400270336,46222559477760,

%T 9302629468471296,2229557114964541440,627125152804037984256,

%U 204500159955172086251520,76507021194866780553609216,32543054888758773094023168000,15614979509514628186072128946176

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

%F 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).

%F a(n) = (1/120) * (64*A000182(n+1) + 20*A000182(n+2) + A000182(n+3)).

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

%Y Cf. A000182, A326327, A385343.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 20 2026