OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Wikipedia, Jacobi polynomials
FORMULA
(n+2) * a(n) = 2^(2+floor(n/2)-floor((n+1)/2)) * (2n+1) * a(n-1) - 4 * (n-1) * a(n-2), with a(0)=1 and a(1)=2. - Sean A. Irvine, Aug 14 2019
From Vaclav Kotesovec, Jan 09 2023: (Start)
Recurrence: (n+1)*(n+2)*(2*n-3)*a(n) = 12*(2*n-1)*(2*n^2 - 2*n - 1)*a(n-2) - 16*(n-3)*(n-2)*(2*n+1)*a(n-4).
a(n) ~ 2^(n-1) * (1 + sqrt(2))^(n + 1/2) * (3 + 2*sqrt(2) + (-1)^n) / (sqrt(Pi) * n^(3/2)). (End)
MAPLE
A025176 := proc(n)
JacobiP(n, 1, 1, sqrt(2)) ;
%*2^(n/2+floor(n/2))/(n+1) ;
simplify(%) ;
end proc: # R. J. Mathar, Feb 05 2013
MATHEMATICA
Table[ 2^(n/2+Floor[ n/2 ])/(n+1)JacobiP[ n, 1, 1, Sqrt[ 2 ] ], {n, 0, 24} ]
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved