A103870 a(n) = Sum_{k=0..n} binomial(2*n,k)*binomial(n,k)*binomial(2*k,n).

1, 4, 44, 580, 8428, 129504, 2063996, 33752576, 562597100, 9516705808, 162878088544, 2814359798936, 49015445212156, 859377160206400, 15153426645082560, 268521098568718080, 4778754834452368620, 85368326032573042800, 1530167828649835039280, 27509703980465935998896

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Formula

Recurrence: 3*n^2*(3*n-2)*(3*n-1)*(77*n^2 - 209*n + 142)*a(n) = (37345*n^6 - 176055*n^5 + 326171*n^4 - 302717*n^3 + 148556*n^2 - 36660*n + 3600)*a(n-1) + 128*(n-1)^2*(2*n-3)^2*(77*n^2 - 55*n + 10)*a(n-2). - Vaclav Kotesovec, Mar 02 2014

a(n) ~ 4 * (512/27)^n / (sqrt(21)*Pi*n). - Vaclav Kotesovec, Mar 02 2014

Mathematica

Table[Sum[Binomial[2*n, k]*Binomial[n, k]*Binomial[2*k, n], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 02 2014 *)

Crossrefs

Sequence in context: A222288 A053315 A005721 * A371680 A056063 A218224

Adjacent sequences: A103867 A103868 A103869 * A103871 A103872 A103873

Keyword

nonn

Author

Detlef Pauly (dettodet(AT)yahoo.de), Nov 08 2001

Extensions

Edited by N. J. A. Sloane, Aug 31 2008 at the suggestion of Jeffrey Shallit

Name edited by Michel Marcus, Jan 31 2023

Status

approved