|
Search: id:A114876
|
|
|
| A114876 |
|
Numerator of the discriminant of the n-th Legendre polynomial. |
|
+0
2
|
|
| 1, 4, 108, 442368, 51200000, 52428800000, 43177371238400000, 60766747818779941065981952, 23542283154891408151173909109014528, 60268244876522004867005207319077191680000000000
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The denominator is A114877. It appears that every prime <= 2n-1 is a factor of the numerator or denominator of the discriminant d(n).
|
|
LINKS
|
Eric Weisstein's World of Mathematics, MathWorld: Polynomial Discriminant
Eric Weisstein's World of Mathematics, MathWorld: Legendre Polynomial
|
|
FORMULA
|
Let d(1)=1 and d(n) = d(n-1) n^(2n-2) (2n-1)^(3-2n). Then a(n)=numer(d(n)).
|
|
EXAMPLE
|
1, 4/3, 108/125, 442368/2100875, 51200000/2977309629, 52428800000/118890080527911,... = A114876/A114877
|
|
CROSSREFS
|
Cf. A114877.
Sequence in context: A107048 A002109 A076265 this_sequence A037980 A015100 A061454
Adjacent sequences: A114873 A114874 A114875 this_sequence A114877 A114878 A114879
|
|
KEYWORD
|
easy,frac,nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Jan 03 2006
|
|
|
Search completed in 0.002 seconds
|
