login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324568 a(n) = Sum_{i=0..n, j=0..n} (binomial(2*i, j) + binomial(2*j, i)). 1

%I #3 Mar 08 2019 03:01:56

%S 2,8,32,124,482,1882,7380,29036,114530,452638,1791638,7100430,

%T 28167986,111837902,444351292,1766536044,7026526226,27960911422,

%U 111308958942,443258277254,1765690504666,7035402933402,28039342445582,111773962249054,445654589001882

%N a(n) = Sum_{i=0..n, j=0..n} (binomial(2*i, j) + binomial(2*j, i)).

%F Recurrence: 2*(n+1)*(5*n^2 - 21*n + 20)*a(n) = (85*n^3 - 332*n^2 + 243*n + 100)*a(n-1) - 3*(65*n^3 - 298*n^2 + 377*n - 100)*a(n-2) + 2*(20*n^3 - 109*n^2 + 191*n - 100)*a(n-3) + 8*(2*n - 5)*(5*n^2 - 11*n + 4)*a(n-4).

%F a(n) ~ 4^(n+1)/3 * (1 + 5/(3*sqrt(Pi*n))).

%t Table[Sum[Binomial[2*i, j] + Binomial[2*j, i], {i, 0, n}, {j, 0, n}], {n, 0, 30}]

%Y Cf. A000984, A006134, A007685, A324566, A324567.

%K nonn

%O 0,1

%A _Vaclav Kotesovec_, Mar 07 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)