A333772 a(n) = n * 2^n * (n!)^2.

2, 32, 864, 36864, 2304000, 199065600, 22759833600, 3329438515200, 606790169395200, 134842259865600000, 35895009576222720000, 11277559372311429120000, 4129466323494701629440000, 1743270091026070964797440000, 840505222458998500884480000000

Offset: 1

Author

Frank Ellermann, Apr 05 2020

Keywords

• nonn

Comments

Sum_{n>=1} a(n) / (2*n)! = Pi + 3.

Examples

			a(2) = 2 * 2^2 * ( 2! )^2 = 2 * 4 * 4 = 32.
a(3) = 3 * 2^3 * ( 3! )^2 = 3 * 8 * 36 = 864.
Sum_{n=1..10} a(n) / ( 2n )! = 3 + 3.01310...
Sum_{n=1..12} a(n) / ( 2n )! = 3 + 3.10046...
Sum_{n=1..18} a(n) / ( 2n )! = 3 + 3.14046...
Sum_{n=1..20} a(n) / ( 2n )! = 3 + 3.14126...
Sum_{n=1..23} a(n) / ( 2n )! = 3 + 3.14154...
		

Links

• Simon Plouffe, On the computation of the n'th decimal digit of various transcendental numbers, arXiv:0912.0303 [math.NT], 2009.

Crossrefs

Cf. A001044 ( (n!)^2 ), A010050 ( (2n)! ), A000796 (digits of Pi).

Programs

Mathematica

Table[n*2^n*(n!)^2,{n,20}] (* Harvey P. Dale, Jun 01 2024 *)

Rexx

S = 2
do N = 2 while length( S ) < 255
   S = S || ', ' || N * ( 2 ** N ) * ( !( N ) ** 2 )
end N
say S                         ;  return S