|
|
A144124
|
|
P_4(2n+1), the Legendre polynomial of order 4 at 2n+1.
|
|
2
|
|
|
1, 321, 2641, 10321, 28401, 63601, 124321, 220641, 364321, 568801, 849201, 1222321, 1706641, 2322321, 3091201, 4036801, 5184321, 6560641, 8194321, 10115601, 12356401, 14950321, 17932641, 21340321, 25212001, 29588001
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
Legendre polynomial LP_4(x) = (35*x^4 - 30*x^2 + 3)/8. - Klaus Brockhaus, Nov 21 2009
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 70*n^4 + 140*n^3 + 90*n^2 + 20*n + 1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 1680 for n > 3; a(0)=1, a(1)=321, a(2)=2641, a(3)=10321.
G.f.: (1 + 316*x + 1046*x^2 + 316*x^3 + x^4)/(1-x)^5. (End)
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) P<x> := PolynomialRing(IntegerRing()); LP_4<x>:=LegendrePolynomial(4); [ Evaluate(LP_4, 2*n+1): n in [0..25] ]; // Klaus Brockhaus, Nov 21 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|