A147291 a(n) = Sum_{k=1..n^2-1} binomial(2k,k).

0, 28, 17576, 209295260, 43308802158650, 150315393336149895056, 8610524734277600186228691452, 8068213695203463278728832778415607708, 122985780058082302876789680971972469134558550878, 30386103720799858392019761983012781659021124133753353112778

Offset: 1

Author

N. J. A. Sloane, Apr 25 2009

Keywords

• nonn

Links

• D. Callan, Divisibility of a Central Binomial Sum: A11292 and A11307, Amer. Math. Monthly, 116 (2009), 468-470.

Crossrefs

Cf. A146977, A066796, A147304.

Programs

Mathematica

Table[Sum[Binomial[2*k, k], {k, 1, n^2 - 1}], {n, 1, 10}] (* Vaclav Kotesovec, Jun 07 2019 *)

PARI

a(n) = sum(k=1, n^2-1, binomial(2*k,k)); \\ Michel Marcus, Jul 05 2018

Formula

a(n) ~ 4^(n^2) / (3*sqrt(Pi)*n). - Vaclav Kotesovec, Jun 07 2019