

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
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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

Table of n, a(n) for n=1..14.


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(pm)<=1  polsturm(pm1)>1, error("increase realprecision")); m+1} \\ Max Alekseyev, Oct 18 2008


CROSSREFS

Sequence in context: A221148 A317664 A062779 * A013042 A190196 A065140
Adjacent sequences: A077152 A077153 A077154 * A077156 A077157 A077158


KEYWORD

nonn


AUTHOR

Benoit Cloitre, Nov 29 2002


EXTENSIONS

a(5)a(13) from Max Alekseyev, Oct 18 2008


STATUS

approved



