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%I #14 Apr 27 2024 16:39:43
%S 1,4,78,3216,229080,25022880,3884393520,812752093440,220448163358080,
%T 75225258805132800,31537353006189676800,15933924342019634227200,
%U 9548252826112300306406400,6695627848564821490753228800,5431772705577464891946292992000,5047432593984519350928894369792000
%N Central terms of the triangle A116853.
%C a(n) = A116853(2*n,n).
%H Reinhard Zumkeller, <a href="/A246606/b246606.txt">Table of n, a(n) for n = 1..200</a>
%F a(n) = (2*n - 1)!*hypergeom([1 - n], [1 - 2*n], -1). - _Peter Luschny_, Nov 04 2018
%F Conjecture: D-finite with recurrence +(-2*n+3)*a(n) +4*(n-1)*(2*n^2-4*n+1)*a(n-1) +(n-1)*(n-2)*(2*n-1)*a(n-2)=0. - _R. J. Mathar_, Jul 01 2022
%F a(n) ~ sqrt(Pi) * 2^(2*n) * n^(2*n - 1/2) / exp(2*n + 1/2). - _Vaclav Kotesovec_, Mar 08 2023
%p a := n -> (2*n - 1)!*hypergeom([1 - n], [1 - 2*n], -1):
%p seq(simplify(a(n)), n=1..15); # _Peter Luschny_, Nov 04 2018
%o (Haskell)
%o a246606 n = a116853 (2 * n - 1) n
%Y Cf. A000142, A116853.
%K nonn,changed
%O 1,2
%A _Reinhard Zumkeller_, Aug 31 2014
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