A160739 16*P_6(n), 16 times the Legendre Polynomial of order 6 at n.

-5, 16, 10159, 143824, 867211, 3415120, 10373071, 26425744, 59271739, 120704656, 227860495, 404631376, 683245579, 1106013904, 1727242351, 2615311120, 3854919931, 5549499664, 7823790319, 10826585296, 14733641995, 19750758736, 26117017999

Offset: 0

Author

N. J. A. Sloane, Nov 17 2009

Keywords

• sign
• 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. A144126, A160741.

Programs

Magma

[231*n^6 -315*n^4 +105*n^2 -5: n in [0..30]]; // G. C. Greubel, May 02 2018

Maple

A160739 := proc(n)
        16*orthopoly[P](6,n) ;
end proc: # R. J. Mathar, Oct 24 2011

Mathematica

Table[16 LegendreP[6,n],{n,0,40}]

PARI

a(n)=16*pollegendre(6,n) \\ Charles R Greathouse IV, Mar 18 2017

PARI

Vec(-(5 - 51*x - 9942*x^2 - 73222*x^3 - 73047*x^4 - 10047*x^5 - 16*x^6) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Jul 23 2019

Formula

a(n) = 231*n^6 - 315*n^4 + 105*n^2 - 5. - Vaclav Kotesovec, Jul 31 2013

From Colin Barker, Jul 23 2019: (Start)

G.f.: -(5 - 51*x - 9942*x^2 - 73222*x^3 - 73047*x^4 - 10047*x^5 - 16*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.

(End)