A160741 Numerator of P_6(2n), the Legendre polynomial of order 6 at 2n.

-5, 10159, 867211, 10373071, 59271739, 227860495, 683245579, 1727242351, 3854919931, 7823790319, 14733641995, 26117017999, 44040338491, 71215667791, 111123125899, 168143944495, 247704167419, 356428995631, 502307776651, 694869638479, 945369767995

Offset: 0

Author

N. J. A. Sloane, Nov 17 2009

Keywords

• sign
• frac
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A160739, A144126.

Programs

Maple

A160741 := proc(n)
        orthopoly[P](6,2*n) ;
        numer(%) ;
end proc: # R. J. Mathar, Oct 24 2011

Mathematica

Table[Numerator[LegendreP[6,2n]],{n,0,40}]

PARI

a(n)=numerator(pollegendre(6,n+n)) \\ Charles R Greathouse IV, Oct 24 2011

PARI

Vec(-(5 - 10194*x - 795993*x^2 - 4516108*x^3 - 4515933*x^4 - 796098*x^5 - 10159*x^6) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Jul 23 2019

Formula

From Colin Barker, Jul 23 2019: (Start)

G.f.: -(5 - 10194*x - 795993*x^2 - 4516108*x^3 - 4515933*x^4 - 796098*x^5 - 10159*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.

a(n) = -5 + 420*n^2 - 5040*n^4 + 14784*n^6.

(End)