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%I #10 Jul 05 2018 05:17:39
%S 1,1,19,239,3011,38435,496365,6470385,84975315,1122708899,14906800361,
%T 198740733581,2658870294349,35677678567549,479965685669059,
%U 6471364940381007,87425255326277907,1183139999323074963,16036589185819644633,217668383345249016045
%N a(n) = (-1)^n*hypergeom([-n, n - 1/2], [1], 4).
%H Robert Israel, <a href="/A299864/b299864.txt">Table of n, a(n) for n = 0..875</a>
%F From _Robert Israel_, Mar 21 2018: (Start)
%F a(n) = JacobiP(n,0,-3/2,-7).
%F n*(2*n-3)*(4*n-7)*a(n)+(2*n-5)*(n-1)*(4*n-3)*a(n-2)-(4*n-5)*(28*n^2-70*n+39)*a(n-1) = 0. (End)
%F a(n) ~ sqrt(3) * (1 + sqrt(3))^(4*n - 1) / (2^(2*n + 1) * sqrt(Pi*n)). - _Vaclav Kotesovec_, Jul 05 2018
%p seq((-1)^n*orthopoly[P](n,0,-3/2,-7),n=0..100); # _Robert Israel_, Mar 21 2018
%t a[n_] := (-1)^n Hypergeometric2F1[-n, n - 1/2, 1, 4]; Table[a[n], {n, 0, 19}]
%Y Cf. A299507, A245926, A084768, A245927.
%Y Cf. A300945, A300946.
%K nonn
%O 0,3
%A _Peter Luschny_, Mar 16 2018
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