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%I #17 Feb 27 2023 08:21:57
%S 0,24,1120,33264,823680,18475600,389398464,7862853600,153876579840,
%T 2940343837200,55138611528000,1018383898440480,18574619721465600,
%U 335240928272918304,5996573430996184960,106438123408375281600,1876607120325212706816,32891715945378106711440
%N A double binomial sum involving absolute values.
%C A fast algorithm follows from Theorem 1 of Brent et al. article.
%H Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, Helmut Prodinger, <a href="http://arxiv.org/abs/1411.1477">Some binomial sums involving absolute values</a>, arXiv:1411.1477v2 [math.CO], 2016.
%F a(n) = Sum_{k=-n..n} (Sum_{l=-n..n} binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k-l)^3).
%F 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
%o (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));
%Y Cf. A000984, A002894, A166337, A268147.
%K easy,nonn
%O 0,2
%A _Richard P. Brent_, Jan 27 2016
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