OFFSET
0,2
COMMENTS
There is a ball-hating monster that lives in a box. You throw 4 numbered balls into the box. He throws 2 balls out. Repeat. Then a(n) gives the number of ordered possibilities the monster has to throw the balls back at each stage (2,1 is different from 1,2).
LINKS
FORMULA
a(n) = (4*n)!/(4*n-2)! for n>0.
a(n) = 32*n + a(n-1) - 20 (with a(0)=0). - Vincenzo Librandi, Nov 13 2010
From Colin Barker, Jun 25 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: 4*x*(3+5*x)/(1-x)^3. (End)
Sum_{n>=1} 1/a(n) = 3*log(2)/4 - Pi/8. - Amiram Eldar, Jan 03 2022
EXAMPLE
a(2) = (4*2)!/(4*2-2)! = 8!/6! = 8*7 = 56.
MAPLE
for n from 1 to 100 do printf(`%d, `, (4*n-4)*(4*n-5)) od: # James A. Sellers, Apr 10 2005
PROG
(PARI) a(n)=4*n*(4*n-1) \\ Charles R Greathouse IV, Jun 16 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ruppi Rana (ruppi.rana(AT)gmail.com), Mar 12 2005
EXTENSIONS
More terms from James A. Sellers, Apr 10 2005
Simpler definition from Ralf Stephan, May 20 2007
STATUS
approved