A105952 (2n)-th Legendre polynomial P_{2n}(x), evaluated at x = 2n-1. Here the Legendre polynomials are normalized so that P_{n}(1) = 1.

1, 321, 213445, 278905249, 610897146201, 2023268287369681, 9449986579423765453, 59214605458489033180545, 479530506556330198532943409, 4875296429727384973283863144801

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..175

Formula

a(n) ~ n^(2*n)*2^(4*n)/(exp(1)*sqrt(2*Pi*n)). - Vaclav Kotesovec, Jul 31 2013

Example

P_{4}(x) = 35/8*x^4 - 15/4*x^2 + 3/8; evaluating at x=3 gives 321.

Maple

with(orthopoly, P); seq(P(2*n, 2*n-1), n=1..12);

Mathematica

Table[LegendreP[2*n, 2*n-1], {n, 1, 20}] (* Vaclav Kotesovec, Jul 31 2013 *)

Prog

(PARI) a(n)=pollegendre(2*n, 2*n-1) \\ Charles R Greathouse IV, Mar 19 2017

Crossrefs

Sequence in context: A074350 A144124 A090101 * A062205 A054034 A357118

Adjacent sequences: A105949 A105950 A105951 * A105953 A105954 A105955

Keyword

easy,nonn

Author

Isabel C. Lugo (izzycat(AT)gmail.com), Apr 27 2005

Status

approved