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

0,1

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).

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)

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}]

Prog

(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

Crossrefs

Cf. A160739, A144126.

Sequence in context: A109514 A022918 A212617 * A101846 A292742 A376103

Adjacent sequences: A160738 A160739 A160740 * A160742 A160743 A160744

Keyword

sign,frac,easy

Author

N. J. A. Sloane, Nov 17 2009

Status

approved