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

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..875

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

Maple

seq((-1)^n*orthopoly[P](n, 0, -3/2, -7), n=0..100); # Robert Israel, Mar 21 2018

Mathematica

a[n_] := (-1)^n Hypergeometric2F1[-n, n - 1/2, 1, 4]; Table[a[n], {n, 0, 19}]

Crossrefs

Cf. A299507, A245926, A084768, A245927.

Cf. A300945, A300946.

Sequence in context: A114757 A142615 A021814 * A025933 A107203 A021544

Adjacent sequences: A299861 A299862 A299863 * A299865 A299866 A299867

Keyword

nonn

Author

Peter Luschny, Mar 16 2018

Status

approved