A034269 a(n) = f(n,n+2) where f is given in A034261.

0, 1, 11, 76, 435, 2255, 11011, 51688, 236028, 1056210, 4654430, 20266312, 87402185, 374008635, 1590144675, 6724160400, 28303504680, 118665923310, 495820606410, 2065492595400, 8581809094950, 35572994871414, 147149351758926, 607555878211376, 2504288265509800

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy
• changed

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A034261.

Programs

Mathematica

Table[n*(n^2+3*n+1)*Binomial[2*n+2,n]/((n+3)*(n+4)),{n,0,20}] (* Vaclav Kotesovec, Oct 27 2012 *)

PARI

a(n)=n*(n^2+3*n+1)*binomial(2*n+2,n)/((n+3)*(n+4)); \\ Joerg Arndt, May 04 2013

Formula

Appears to be a(n) = 4^(n+1)*Pi^(-1/2)*Gamma(n+3/2)/Gamma(n+5)*(n+1)*n*(n^2+3*n+1). - Mark van Hoeij, Oct 30 2011

a(n) ~ 2^(2*n+2) * sqrt(n/Pi). - Amiram Eldar, Sep 04 2025

Extensions

Corrected and extended by N. J. A. Sloane, Apr 21 2000