A099869 - OEIS

%I #14 May 12 2013 05:01:04

%S 1,4,23,197,2056,23714,290512,3707852,48760367,656043857,8987427467,

%T 124936258127,1757900019101,24987199492705,358268702159069,

%U 5175497420902741,75254198337177848,1100534370899151722,16176618251666906476,238861285363295350240

%N Bisection of A014137.

%H Vincenzo Librandi, <a href="/A099869/b099869.txt">Table of n, a(n) for n = 0..200</a>

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

%F Recurrence: n*(2*n+1)*a(n) = 3*(2*n^2+13*n-8)*a(n-1) + 6*(74*n^2 - 305*n + 298)*a(n-2) - 28*(4*n-9)*(4*n-7)*a(n-3). - _Vaclav Kotesovec_, Oct 17 2012

%F a(n) ~ 2^(4*n+1/2)/(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): seq(a(n),n=0..20); # _Emeric Deutsch_

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

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

%Y Cf. A014137, A099975, A000108.

%K nonn,easy

%O 0,2

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

%E More terms from _Emeric Deutsch_, Dec 20 2004