OFFSET
0,1
COMMENTS
Also powers of 2 with singly even numbers (A016825) as exponents. - Alonso del Arte, Sep 03 2012
The partial sum of A000888(n) = Catalan(n)^2*(n + 1) resp. A267844(n) = Catalan(n)^2*(4n + 3) resp. A267987(n) = Catalan(n)^2*(4n + 4) divided by A013709(n) (this) a(n) = 2^(4n+2) absolutely converge to 1/Pi resp. 1 resp. 4/Pi. Thus this series is 1/Pi resp. 1 resp. 4/Pi. - Ralf Steiner, Jan 23 2016
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (16).
FORMULA
a(n) = 16*a(n-1), n > 0; a(0) = 4. G.f.: 4/(1 - 16*x). [Philippe Deléham, Nov 23 2008]
a(n) = 4^(2*n + 1) = 2^(4*n + 2). - Alonso del Arte, Sep 03 2012
a(n) = 4*A001025(n). - Michel Marcus, Jan 30 2016
From Elmo R. Oliveira, Aug 26 2024: (Start)
E.g.f.: 4*exp(16*x).
MAPLE
MATHEMATICA
2^(4 Range[0, 15] + 2) (* Alonso del Arte, Sep 03 2012 *)
NestList[16#&, 4, 20] (* Harvey P. Dale, Jun 03 2013 *)
PROG
(Magma) [4^(2*n+1): n in [0..20]]; // Vincenzo Librandi, May 26 2011
(PARI) a(n)=4<<(4*n) \\ Charles R Greathouse IV, Apr 07 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved