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A190315 Central coefficients of the Riordan matrix ((1-x-x^2)/(1-2x-x^2),(x-x^2-x^3)/(1-2x-x^2)) (A190215).

%I A190315 #22 Mar 05 2018 04:10:28
%S A190315 1,2,9,48,265,1500,8638,50360,296325,1756160,10467556,62683896,
%T A190315 376838098,2272896626,13747543035,83354081728,506467851061,
%U A190315 3083121435312,18799746616104,114804614071760,702016963933404,4297947201746176,26342178216979384
%N A190315 Central coefficients of the Riordan matrix ((1-x-x^2)/(1-2x-x^2),(x-x^2-x^3)/(1-2x-x^2)) (A190215).
%H A190315 G. C. Greubel, <a href="/A190315/b190315.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 from Vincenzo Librandi)
%F A190315 a(n) = T(2*n,n), where T(n,k)=A190215(n,k).
%F A190315 a(n) = Sum_{i=0..n} binomial(n+i,n)*Sum_{j=0..n-i} binomial(i+j-1,j)*binomial(j,n-i-j).
%t A190315 Table[Sum[Binomial[n+i,n]Sum[Binomial[i+j-1,j]Binomial[j,n-i-j],{j,0,n-i}],{i,0,n}],{n,0,22}]
%o A190315 (Maxima) makelist(sum(binomial(n+i,n)*sum(binomial(i+j-1,j)*binomial(j,n-i-j),j,0,n-i),i,0,n),n,0,22);
%o A190315 (PARI) for(n=0,30, print1(sum(k=0,n, binomial(n+k,n)*sum(j=0,n-k, binomial(k+j-1,j)*binomial(j,n-k-j))), ", ")) \\ _G. C. Greubel_, Mar 04 2018
%Y A190315 Cf. A190215.
%K A190315 nonn
%O A190315 0,2
%A A190315 _Emanuele Munarini_, May 10 2011