|
|
A140870
|
|
8*P_4(2n), 8 times the Legendre Polynomial of order 4 at 2n.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
Legendre polynomial LP_4(x) = (35*x^4-30*x^2+3)/8. - Klaus Brockhaus, Nov 21 2009
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)
|
|
MAPLE
|
8*orthopoly[P](4, 2*n) ;
|
|
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 *)
|
|
PROG
|
(Magma)
P<x> := PolynomialRing(IntegerRing());
LP4:=LegendrePolynomial(4);
(PARI) {for(n=0, 26, print1(subst(8*pollegendre(4), x, 2*n), ", "))} \\ Klaus Brockhaus, Nov 21 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|