Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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