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A102224
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Column 0 of the matrix square of A102220, which equals the lower triangular matrix: [2*I - A008459]^(-1).
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0
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1, 2, 14, 200, 4814, 174752, 8909168, 606818060, 53211837134, 5838211285616, 783434682568664, 126221710572107900, 24043148814317769584, 5344827109234104188348, 1371307353540074156012828
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OFFSET
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0,2
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COMMENTS
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Triangle A008459 consists of the squared binomial coefficients.
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LINKS
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FORMULA
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Sum_{n>=0} a(n)*x^n/n!^2 = 1/(2-BesselI(0,2*sqrt(x)))^2. - Vladeta Jovovic, Jul 17 2006
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EXAMPLE
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Given A102221 = [1,1,5,55,1077,32951,1451723,87054773,...], then this sequence results from a type of self-convolution of A102221:
a(2) = 14 = 1^2*1*5 + 2^2*1*1 + 1^2*5*1,
a(3) = 200 = 1^2*1*55 + 3^2*1*5 + 3^2*5*1 + 1^2*55*1.
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PROG
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(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]}
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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