A055218 - OEIS

%I #18 May 24 2017 02:37:41

%S 1,4,15,51,168,540,1711,5365,16698,51679,159250,489048,1497681,

%T 4576140,13955895,42493677,129211818,392441049,1190716836,3609608838,

%U 10933915743,33097421223,100126350090,302737691646,914897836063

%N a(n) = T(2*n+2,n), array T as in A055216.

%H G. C. Greubel, <a href="/A055218/b055218.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: ((2*x-1) *sqrt(-3*x^2-2*x+1)+2*x^3-3*x+1)/ (6*x^6+x^5 +sqrt(-3*x^2-2*x+1) *(3*x^4-x^3)-4*x^4+x^3). - _Vladimir Kruchinin_, May 24 2014

%F a(n) ~ 3^(n+2)/2 * (1-3*sqrt(3)/(2*sqrt(Pi*n))). - _Vaclav Kotesovec_, May 24 2014

%t Table[Sum[Binomial[n+2,i]*Sum[Binomial[i,j],{j,0,n-i}],{i,0,n+2}],{n,0,20}] (* _Vaclav Kotesovec_, May 24 2014 *)

%o (PARI) x='x+O('x^50); Vec(((2*x-1)*sqrt(-3*x^2-2*x+1)+2*x^3-3*x+ 1)/(6*x^6 +x^5 + sqrt(-3*x^2-2*x+1)*(3*x^4-x^3)-4*x^4+x^3)) \\ _G. C. Greubel_, May 23 2017

%Y Cf. A055216.

%K nonn

%O 0,2

%A _Clark Kimberling_, May 07 2000