A025163 The value of the associated Legendre Polynomial of index n and order 1 evaluated at x=2^(-1/2) multiplied by 2^(3*n/2-1).

0, 1, 6, 18, 20, -90, -588, -1708, -1944, 7110, 47300, 136092, 156312, -528164, -3540600, -10141080, -11703344

Offset: 0

Author

Wouter Meeussen

Keywords

• sign

Comments

Conjecture: (-n+1)*a(n) +2*(2*n-1)*a(n-1) -8*n*a(n-2)=0. - R. J. Mathar, Feb 05 2013

This recurrence follows from the contiguous relation that relates the three Legendre Polynomials of the same order. Wouter Meeussen, Feb 06 2013

Links

• Wikipedia, Associated Legendre Polynomials

Programs

Mathematica

Table[ -2^(-1 + (3*n)/2)*LegendreP[ n, 1, 1/Sqrt[ 2 ] ], {n, 0, 16} ]