|
|
A077155
|
|
Let p(2n+1,x)=(x+1)(x+2)...(x+2n)(x+2n+1), a(n) is the smallest integer >0 such that p(2n+1,x)-k has only one real root for any k >=a(n).
|
|
0
|
|
|
1, 4, 96, 4930, 416615, 52346851, 9150486666, 2122773858331, 630854176216923, 233667907156182198, 105531126177212999940, 57078667671269237092154, 36423221938771375213756343, 27076505528935399371748578683
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n) is the smallest integer strictly greater than the maximum value of p(2n+1,x) in the interval [ -1,-(2n+1)]. Note that this maximum value is attained by p(2n+1,x) at some root of its derivative. - Max Alekseyev, Oct 18 2008
|
|
LINKS
|
|
|
PROG
|
(PARI) {a(n) = local(p, r, m); p=prod(k=1, 2*n+1, x+k); r=real(polroots(deriv(p))); m=vecmax(vector(#r, j, floor(subst(p, x, r[j])))); if( polsturm(p-m)<=1 || polsturm(p-m-1)>1, error("increase realprecision")); m+1} \\ Max Alekseyev, Oct 18 2008
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|