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%I #30 Feb 03 2022 08:52:31
%S 1,3,40,1050,42336,2328480,163088640,13913499600,1401656256000,
%T 162984589447680,21497802046156800,3172717285311974400,
%U 518147911684085760000,92790773980160256000000,18083066033253630689280000,3810158522787893903827200000
%N a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3).
%C Central terms of the triangle A247500.
%H Reinhard Zumkeller, <a href="/A204515/b204515.txt">Table of n, a(n) for n = 0..250</a>
%H G.-N. Han and H. Xiong, <a href="http://arxiv.org/abs/1508.00772">Difference operators for partitions and some applications</a>, arXiv preprint arXiv:1508.00772 [math.CO], 2015-2018.
%F a(n) = A248045(n+1) / (n+1).
%t Table[((2n)!(2n+1)!)/((n+1)^2 n!^3),{n,0,20}] (* _Harvey P. Dale_, May 17 2019 *)
%o (Haskell)
%o a204515 n = a247500 (2 * n) n
%o (PARI) a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3); \\ _Michel Marcus_, Feb 03 2022
%Y Cf. A000142, A247500, A248045.
%K nonn
%O 0,2
%A _Reinhard Zumkeller_, Oct 19 2014
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