A099975 - OEIS

%I #18 Aug 19 2019 10:10:28

%S 2,9,65,626,6918,82500,1033412,13402697,178405157,2423307047,

%T 33453694487,467995871777,6619846420553,94520750408709,

%U 1360510918810437,19720133460129650,287590328749420958,4216819865806452984,62127422576288648840,919286657093271150630

%N Bisection of A014137.

%H Vincenzo Librandi, <a href="/A099975/b099975.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) = sum(binomial(2k, k)/(k+1), k=0..2n+1). - _Emeric Deutsch_, Dec 20 2004

%F Recurrence: (n+1)*(2*n+1)*a(n) = 3*(2*n^2 + 15*n - 1)*a(n-1) + 6*(74*n^2 - 231*n + 164)*a(n-2) - 28*(4*n-7)*(4*n-5)*a(n-3). - _Vaclav Kotesovec_, Oct 17 2012

%F a(n) ~ 2^(4*n+5/2)/(3*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 17 2012

%p a:=n->sum(binomial(2*k,k)/(k+1),k=0..2*n+1): seq(a(n),n=0..20); # _Emeric Deutsch_, Dec 20 2004

%t Table[Sum[Binomial[2k,k]/(k+1),{k,0,2*n+1}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 17 2012 *)

%o (PARI) a(n)=sum(k=0,2*n+1, binomial(2*k,k)/(k+1)); \\ _Joerg Arndt_, May 12 2013

%Y Cf. A014137, A099975.

%Y Cf. A000108.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Nov 19 2004

%E More terms from _Emeric Deutsch_, Dec 20 2004