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%I #12 Jul 09 2017 17:22:25
%S 1,2,14,200,4814,174752,8909168,606818060,53211837134,5838211285616,
%T 783434682568664,126221710572107900,24043148814317769584,
%U 5344827109234104188348,1371307353540074156012828
%N Column 0 of the matrix square of A102220, which equals the lower triangular matrix: [2*I - A008459]^(-1).
%C A102221 is column 0 of A102220.
%C Triangle A008459 consists of the squared binomial coefficients.
%F a(n) = Sum_{k=0..n} C(n, k)^2*A102221(k)*A102221(n-k).
%F Sum_{n>=0} a(n)*x^n/n!^2 = 1/(2-BesselI(0,2*sqrt(x)))^2. - _Vladeta Jovovic_, Jul 17 2006
%e Given A102221 = [1,1,5,55,1077,32951,1451723,87054773,...], then this sequence results from a type of self-convolution of A102221:
%e a(2) = 14 = 1^2*1*5 + 2^2*1*1 + 1^2*5*1,
%e a(3) = 200 = 1^2*1*55 + 3^2*1*5 + 3^2*5*1 + 1^2*55*1.
%o (PARI) {a(n)=(matrix(n+1,n+1,i,j,if(i==j,2,0)-binomial(i-1,j-1)^2)^-2)[n+1,1]}
%Y Cf. A102220, A102221, A008459.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Dec 31 2004
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