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A190155 Central coefficients of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-x^2-sqrt(1-2*x-5*x^2+2*x^3+x^4))/(2*x^2) (A132276).

%I A190155 #15 Feb 14 2025 02:55:27
%S A190155 1,2,12,64,385,2346,14672,92936,595179,3841970,24959726,162988464,
%T A190155 1068860884,7034520304,46437268905,307351081056,2038878634695,
%U A190155 13552394472612,90242046694715,601847594327000,4019556724362165,26879647264387170
%N A190155 Central coefficients of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-x^2-sqrt(1-2*x-5*x^2+2*x^3+x^4))/(2*x^2) (A132276).
%H A190155 G. C. Greubel, <a href="/A190155/b190155.txt">Table of n, a(n) for n = 0..750</a> (terms 0..100 from Vincenzo Librandi)
%F A190155 a(n) = T(2*n,n) where T(n,k) = A132276(n,k).
%F A190155 a(n) = Sum_{i=0..(n/2)} ( binomial(n+2*i,i)*((n+1)/(i+n+1)) * Sum_{j=0..(n-2*i)} binomial(2*n-j,n+2*i)*binomial(n-2*i-j,j) ).
%t A190155 Table[Sum[Binomial[n+2i,i](n+1)/(i+n+1)Sum[Binomial[2n-j,n+2i]Binomial[n-2i-j,j],{j,0,n-2i}],{i,0,n/2}],{n,0,21}]
%o A190155 (Maxima) makelist(sum(binomial(n+2*i,i)*(n+1)/(i+n+1)*sum(binomial(2*n-j,n+2*i)*binomial(n-2*i-j,j),j,0,n-2*i),i,0,n/2),n,0,21);
%o A190155 (PARI) for(n=0,30, print1(sum(i=0,n/2, binomial(n+2*i,i)*((n+1)/(i+n+1)) *sum(j=0, n-2*i, binomial(2*n-j,n+2*i)*binomial(n-2*i-j,j))), ", ")) \\ _G. C. Greubel_, Dec 28 2017
%Y A190155 Cf. A132276.
%K A190155 nonn,easy
%O A190155 0,2
%A A190155 _Emanuele Munarini_, May 05 2011