A160743 8*P_7(n), 8 times the Legendre Polynomial of order 7 at n.

0, 8, 17593, 389112, 3169562, 15694600, 57385803, 170880248, 438565492, 1005601032, 2110507325, 4124403448, 7599974478, 13331249672, 22425272527, 36386743800, 57216718568, 87526438408, 130667379777, 190878599672, 273452459650, 384919809288, 533255710163

Offset: 0

Author

N. J. A. Sloane, Nov 17 2009

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Programs

Maple

A160743 := proc(n)
        8*orthopoly[P](7,n) ;
end proc: # R. J. Mathar, Oct 24 2011

Mathematica

Table[8 LegendreP[7,n],{n,0,50}]

PARI

a(n)=pollegendre(7,n)<<3 \\ Charles R Greathouse IV, Oct 24 2011

PARI

concat(0, Vec(x*(8 + 17529*x + 248592*x^2 + 548822*x^3 + 248592*x^4 + 17529*x^5 + 8*x^6) / (1 - x)^8 + O(x^40))) \\ Colin Barker, Jul 23 2019

Formula

a(n) = n*(429*n^6 - 693*n^4 + 315*n^2 - 35)/2. - Vaclav Kotesovec, Jul 31 2013

From Colin Barker, Jul 23 2019: (Start)

G.f.: x*(8 + 17529*x + 248592*x^2 + 548822*x^3 + 248592*x^4 + 17529*x^5 + 8*x^6) / (1 - x)^8.

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>7.

(End)