A140870 8*P_4(2n), 8 times the Legendre Polynomial of order 4 at 2n.

3, 443, 8483, 44283, 141443, 347003, 721443, 1338683, 2286083, 3664443, 5588003, 8184443, 11594883, 15973883, 21489443, 28323003, 36669443, 46737083, 58747683, 72936443, 89552003, 108856443, 131125283, 156647483, 185725443, 218675003, 255825443

Offset: 0

Author

N. J. A. Sloane, Nov 17 2009

Keywords

• nonn
• easy

Links

• Eric W. Weisstein, Legendre Polynomial.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A144124.

Programs

Magma

P := PolynomialRing(IntegerRing());
LP4:=LegendrePolynomial(4);
[ Evaluate(8*LP4, 2*n): n in [0..26] ]; // Klaus Brockhaus, Nov 18 2009

Magma

[560*n^4 - 120*n^2 + 3: n in [0..30]]; // Vincenzo Librandi, Oct 04 2015

Maple

A140870 := proc(n)
        8*orthopoly[P](4,2*n) ;
end proc: # R. J. Mathar, Oct 24 2011

Mathematica

Table[8 LegendreP[4,2n],{n,0,50}]
LinearRecurrence[{5, -10, 10, -5, 1}, {3, 443, 8483, 44283, 141443}, 30] (* Vincenzo Librandi, Oct 04 2015 *)

PARI

{for(n=0, 26, print1(subst(8*pollegendre(4), x, 2*n), ","))} \\ Klaus Brockhaus, Nov 21 2009

Formula

Legendre polynomial LP_4(x) = (35*x^4-30*x^2+3)/8. - Klaus Brockhaus, Nov 21 2009

From Klaus Brockhaus, Nov 21 2009: (Start)

a(n) = 560*n^4-120*n^2+3.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4)+13440 for n > 3; a(0)=3, a(1)=443, a(2)=8483, a(3)=44283.

G.f.: (3+428*x+6298*x^2+6268*x^3+443*x^4)/(1-x)^5. (End)