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Search: id:A108626
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| A108626 |
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Antidiagonal sums of square array A108625, in which row n equals the crystal ball sequence for A_n lattice. |
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+0
3
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| 1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919, 125578, 406865, 1322772, 4313155, 14099524, 46192483, 151628090, 498578411, 1641921014, 5414619739, 17878144968, 59097039545, 195548471268, 647665451911, 2146947613286
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Limit a(n+1)/a(n) = 3.3829757679... = 1/r = 3 + r + r^2, where r is radius of convergence of A(x), which diverges at x=r.
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FORMULA
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a(n) = Sum_{k=0..n} Sum_{i=0..k} C(n, i)^2 * C(n+k-i, k-i).
G.f.: A(x) = exp( Sum_{n>=1} A108627(n)*x^n/n ), where A108627 has g.f.: 2*x*(1-x-x^3)/((1-x)*(1-3*x-x^2-x^3)).
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EXAMPLE
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Log(A(x)) = 2*x + 6*x^2/2 + 20*x^3/3 +...+ A108627(n)*x^n/n +...
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PROGRAM
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(PARI) a(n)=sum(k=0, n, sum(i=0, k, binomial(n-k, i)^2*binomial(n-i, k-i)))
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CROSSREFS
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Cf. A108625.
Cf. A108627.
Sequence in context: A088355 A113485 A054391 this_sequence A128739 A036766 A000660
Adjacent sequences: A108623 A108624 A108625 this_sequence A108627 A108628 A108629
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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), Jun 12 2005
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