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A268147
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A double binomial sum involving absolute values.
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4
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0, 16, 512, 12288, 262144, 5242880, 100663296, 1879048192, 34359738368, 618475290624, 10995116277760, 193514046488576, 3377699720527872, 58546795155816448, 1008806316530991104, 17293822569102704640, 295147905179352825856, 5017514388048998039552
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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)^2).
a(n) = n*16^n.
a(n) = 32*a(n-1)-256*a(n-2) for n>1.
G.f.: 16*x / (1-16*x)^2.
(End)
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MAPLE
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a:= proc(n) option remember;
16*`if`(n<2, n, n*a(n-1)/(n-1))
end:
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MATHEMATICA
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LinearRecurrence[{32, -256}, {0, 16}, 20] (* Harvey P. Dale, Jul 19 2018 *)
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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)^2));
(PARI) concat(0, Vec(16*x/(1-16*x)^2 + O(x^20))) \\ Colin Barker, Feb 11 2016
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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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