%I #11 Feb 25 2022 04:25:51

%S 6,1260,2494800,20432412000,475176173472000,25246110096567360000,

%T 2658415393168543008000000,501882242076289234480320000000,

%U 157671325170687025904337331200000000,77811744999685071405945898971187200000000,57616484702466807973246700352205274112000000000

%N a(n) = (4n+3)!/4^n.

%F From _Amiram Eldar_, Feb 25 2022: (Start)

%F Sum_{n>=0} 1/a(n) = (sinh(sqrt(2)) - sin(sqrt(2)))/(4*sqrt(2)).

%F Sum_{n>=0} (-1)^n/a(n) = (cosh(1)*sin(1) - sinh(1)*cos(1))/4. (End)

%t Table[(4n+3)!/4^n,{n,0,20}] (* _Harvey P. Dale_, Mar 14 2020 *)

%o (PARI) a(n) = (4*n+3)!/4^n; \\ _Michel Marcus_, Feb 25 2022

%Y Cf. A052277.

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Feb 05 2000