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Search: id:A102224
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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
1
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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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COMMENT
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A102221 is column 0 of A102220. Triangle A008459 consists of the squared binomial coefficients.
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FORMULA
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a(n) = Sum_{k=0..n} C(n, k)^2*A102221(k)*A102221(n-k).
Sum_{n>=0} a(n)*x^n/n!^2 = 1/(2-BesselI(0,2*sqrt(x)))^2. - Vladeta Jovovic (vladeta(AT)Eunet.yu), 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 A10221:
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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PROGRAM
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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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Cf. A102220, A102221, A008459.
Sequence in context: A132611 A047796 A090300 this_sequence A123543 A054652 A122647
Adjacent sequences: A102221 A102222 A102223 this_sequence A102225 A102226 A102227
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Dec 31 2004
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