A082578 a(n) = Sum_{k=0..n} binomial(2*k, k) * binomial(2*k+1,k).

1, 7, 67, 767, 9587, 126011, 1711595, 23796515, 336666215, 4828084575, 69994481871, 1023793569567, 15086216016367, 223704570996367, 3335098322412367, 49954148031128767, 751296616443141667

Offset: 0

Author

Emanuele Munarini, May 07 2003

Keywords

• easy
• nonn

Comments

Old name was "A binomial sum".

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Partial sums of A000894.

Programs

Mathematica

Table[Sum[Binomial[2k,k]*Binomial[2k+1,k],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, Oct 14 2012 *)

Maxima

makelist(sum(binomial(2*k,k)*binomial(2*k+1,k),k,0,n),n,0,12);

Formula

Recurrence: (n+3)*(n+2)*a(n+2) - (17*n^2+69*n+66)*a(n+1) + (16*n^2+64*n+60)*a(n) = 0.

a(n) ~ 2^(4*n+5)/(15*Pi*n). - Vaclav Kotesovec, Oct 14 2012

Extensions

Name changed by Wesley Ivan Hurt, Apr 18 2023