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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

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(p-m)<=1 || polsturm(p-m-1)>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

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Last modified December 4 21:40 EST 2022. Contains 358570 sequences. (Running on oeis4.)