A076620 Coefficient of x^a(n) in (x+1)*(x+2)*...*(x+n) is the largest one.

0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,7

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

Is a(n) - floor(log(n)) bounded?

Example

In (x+1)(x+2)(x+3) = x^3 + 6*x^2 + 11*x + 6, the largest coefficient (11) appears at x^1, hence a(3)=1.

Prog

(PARI) a(n) = my(p=prod(j=1, n, x+j), m=vecmax(Vec(p))); for (i=0, poldegree(p), if (polcoef(p, i)==m, return(i))); \\ Michel Marcus, Feb 19 2021
(PARI) first(n) = {res = vector(n); my(r = 1); v = [1]; for(i = 1, n, v = concat(0, v) + concat(v, 0)*i; for(j = r + 1, #v, if(v[j] > v[j - 1], r++ , next ); ); res[i] = r-1 ); res } \\ David A. Corneth, Feb 21 2021
(Python)
from sympy import prod, Poly
from sympy.abc import x
def A076620(n):
    y = Poly(prod(x+i for i in range(1, n+1))).all_coeffs()[::-1]
    return y.index(max(y)) # Chai Wah Wu, Mar 07 2021

Crossrefs

Cf. A065048, A130534, A309237.

Sequence in context: A204560 A135661 A082998 * A121900 A333525 A056811

Adjacent sequences: A076617 A076618 A076619 * A076621 A076622 A076623

Keyword

nonn

Author

Benoit Cloitre, Nov 10 2002

Status

approved