A034270 - OEIS

%I #21 Oct 19 2023 19:44:01

%S 0,1,13,99,605,3289,16653,80444,375972,1715130,7681586,33913385,

%T 148018455,640049865,2746422525,11708971560,49647131160,209523969630,

%U 880668859590,3688555690950,15401089588794,64128925255626,266376231244178,1104047701891624,4566956385797400

%N f(n,n+3) where f is given in A034261.

%H Vincenzo Librandi, <a href="/A034270/b034270.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) ~ c*sqrt(n)*4^n, with c = 8/sqrt(Pi) = 2*A249521. - _Stefano Spezia_, Oct 19 2023

%t Table[n*(n^2+4*n+1)*Binomial[2*n+3,n]/((n+4)*(n+5)),{n,0,20}] (* _Vaclav Kotesovec_, Oct 27 2012 *)

%o (Magma) [n*(n^2+4*n+1)*Binomial(2*n+3, n)/((n+4)*(n+5)): n in [0..25]]; // _Vincenzo Librandi_, May 04 2013

%o (PARI) a(n)=n*(n^2+4*n+1)*binomial(2*n+3,n)/((n+4)*(n+5)); \\ _Joerg Arndt_, May 04 2013

%Y Cf. A000302, A034261, A249521.

%K nonn,easy

%O 0,3

%A _Clark Kimberling_

%E Corrected and extended by _N. J. A. Sloane_, Apr 21 2000