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A268149
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A double binomial sum involving absolute values.
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2
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0, 24, 1120, 33264, 823680, 18475600, 389398464, 7862853600, 153876579840, 2940343837200, 55138611528000, 1018383898440480, 18574619721465600, 335240928272918304, 5996573430996184960, 106438123408375281600, 1876607120325212706816, 32891715945378106711440
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OFFSET
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0,2
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COMMENTS
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A fast algorithm follows from Theorem 1 of Brent et al. article.
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LINKS
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FORMULA
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a(n) = Sum_{k=-n..n} (Sum_{l=-n..n} binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k-l)^3).
Conjecture D-finite with recurrence (2*n-1)*(n-1)*a(n) +2*(-22*n^2+27*n-36)*a(n-1) +12*(4*n-5)*(4*n-7)*a(n-2)=0. - R. J. Mathar, Feb 27 2023
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PROG
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(PARI) a(n) = sum(k=-n, n, sum(l=-n, n, binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k-l)^3));
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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