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A191586 Binomial row sums of the Riordan matrix (1/(1-x),x/(1-x^2)) (A046854).

%I A191586 #13 Aug 31 2017 13:43:47
%S A191586 1,2,4,11,32,92,271,814,2464,7508,23024,70952,219503,681358,2121116,
%T A191586 6619571,20703040,64873328,203625604,640109128,2014951552,6350490808,
%U A191586 20037015200,63284778256,200063948527,633007850942,2004431426716,6351693835169,20141013776384
%N A191586 Binomial row sums of the Riordan matrix (1/(1-x),x/(1-x^2)) (A046854).
%H A191586 Vincenzo Librandi, <a href="/A191586/b191586.txt">Table of n, a(n) for n = 0..198</a>
%F A191586 a(n) = Sum_{k=0..n} binomial(n,k)*binomial(floor((n+k)/2),k).
%F A191586 (8*n^2+88*n+240)*a(n+6) - (72*n^2+636*n+1380)*a(n+5) + (180*n^2+1300*n+2232)*a(n+4) - (180*n^2+1170*n+1842)*a(n+3) + (326*n^2+2074*n+3164)*a(n+2) - (228*n^2+948*n+984)*a(n+1) + (35*n^2+105*n+70)*a(n) = 0. - _Emanuele Munarini_, Aug 31 2017
%t A191586 Table[Sum[Binomial[n, k]Binomial[Floor[(n+k)/2],k],{k,0,n}],{n,0,100}]
%o A191586 (Maxima) makelist(sum(binomial(n,k)*binomial(floor((n+k)/2),k),k,0,n),n,0,12);
%Y A191586 Cf. A046854.
%K A191586 nonn,easy
%O A191586 0,2
%A A191586 _Emanuele Munarini_, Jun 07 2011