OFFSET
1,1
COMMENTS
Sum_{n>=1} a(n) / (2*n)! = Pi + 3.
LINKS
Simon Plouffe, On the computation of the n'th decimal digit of various transcendental numbers, arXiv:0912.0303 [math.NT], 2009.
EXAMPLE
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...
MATHEMATICA
Table[n*2^n*(n!)^2, {n, 20}] (* Harvey P. Dale, Jun 01 2024 *)
PROG
(Rexx)
S = 2
do N = 2 while length( S ) < 255
S = S || ', ' || N * ( 2 ** N ) * ( !( N ) ** 2 )
end N
say S ; return S
CROSSREFS
KEYWORD
nonn
AUTHOR
Frank Ellermann, Apr 05 2020
STATUS
approved