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%I #13 Dec 27 2017 01:39:37
%S 1,2,9,48,265,1512,8813,52112,311427,1876290,11376893,69341868,
%T 424445996,2607388252,16066200465,99256947520,614611513599,
%U 3813391239444,23702418040232,147557273500400,919907826138042,5742264749678028,35886019625941713
%N Central coefficients of the Riordan matrix (g(x),x*g(x)), where g(x) = (1-x-sqrt(1-2x-3x^2-4x^3))/(2*x^2*(1+x)) (A190252).
%H G. C. Greubel, <a href="/A190253/b190253.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..122 from Vincenzo Librandi)
%F a(n) = T(2n,n), where T(n,k) = A190252(n,k).
%t Table[Sum[Binomial[n+2i,i]((n+1)/(n+i+1))Sum[Binomial[i,j]Binomial[2n-j,n+2i],{j,0,i}],{i,0,n/2}],{n,0,22}]
%o (Maxima) makelist(sum(binomial(n+2*i,i)*(n+1)/(n+i+1)*sum(binomial(i,j)*binomial(2*n-j,n+2*i),j,0,i),i,0,n/2),n,0,22);
%o (PARI) a(n)=sum(i=0,n\2,binomial(n+2*i,i)*(n+1)/(n+i+1)*sum(j=0,i,binomial(i,j)*binomial(2*n-j,n+2*i))) \\ _Charles R Greathouse IV_, Jun 29 2011
%Y Cf. A190252.
%K nonn
%O 0,2
%A _Emanuele Munarini_, May 06 2011