A299864 a(n) = (-1)^n*hypergeom([-n, n - 1/2], [1], 4).
1, 1, 19, 239, 3011, 38435, 496365, 6470385, 84975315, 1122708899, 14906800361, 198740733581, 2658870294349, 35677678567549, 479965685669059, 6471364940381007, 87425255326277907, 1183139999323074963, 16036589185819644633, 217668383345249016045
Offset: 0
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 0..875
Programs
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Maple
seq((-1)^n*orthopoly[P](n,0,-3/2,-7),n=0..100); # Robert Israel, Mar 21 2018
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Mathematica
a[n_] := (-1)^n Hypergeometric2F1[-n, n - 1/2, 1, 4]; Table[a[n], {n, 0, 19}]
Formula
From Robert Israel, Mar 21 2018: (Start)
a(n) = JacobiP(n,0,-3/2,-7).
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)
a(n) ~ sqrt(3) * (1 + sqrt(3))^(4*n - 1) / (2^(2*n + 1) * sqrt(Pi*n)). - Vaclav Kotesovec, Jul 05 2018