OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = (2^(n-1) + 0^n/2)*C(2*n+2, n).
(n+2)*a(n) +12*(-n-1)*a(n-1) +16*(2*n-1)*a(n-2)=0. - R. J. Mathar, Oct 29 2014
From Amiram Eldar, Jan 16 2024: (Start)
Sum_{n>=0} 1/a(n) = 88*arccot(sqrt(7))/(7*sqrt(7)) - 3/7.
Sum_{n>=0} (-1)^n/a(n) = 52*log(2)/27 - 5/9. (End)
EXAMPLE
a(0)=(2^(-1)+(0^0)/2)C(2,0)=2*(1/2)=1 (use 0^0=1).
MATHEMATICA
Join[{1}, Table[2^(n-1)*Binomial[2*n+2, n], {n, 1, 50}]] (* G. C. Greubel, Feb 05 2018 *)
PROG
(PARI) for(n=0, 30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+2, n), ", ")) \\ G. C. Greubel, Feb 05 2018
(Magma) [(2^(n-1) + 0^n/2)*Binomial(2*n+2, n): n in [0..30]]; // G. C. Greubel, Feb 05 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 06 2003
STATUS
approved