A052278 - OEIS

A052278

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

6, 1260, 2494800, 20432412000, 475176173472000, 25246110096567360000, 2658415393168543008000000, 501882242076289234480320000000, 157671325170687025904337331200000000, 77811744999685071405945898971187200000000, 57616484702466807973246700352205274112000000000

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..10.

FORMULA

From Amiram Eldar, Feb 25 2022: (Start)

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

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

MATHEMATICA

Table[(4n+3)!/4^n, {n, 0, 20}] (* Harvey P. Dale, Mar 14 2020 *)

PROG