A076634 Coefficient of x^a(n) in (x+1/2)*(x+2/2)*...*(x+n/2) is the largest one.

1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7

Offset: 1

Author

Benoit Cloitre, Nov 10 2002

Keywords

• nonn

Crossrefs

Cf. A076620.

Programs

PARI

a(n) = my(p=prod(j=1, n, x+j/2), m=vecmax(Vec(p))); for (i=0, poldegree(p), if (polcoef(p, i)==m, return(i))); \\ Michel Marcus, Feb 19 2021

Python

from sympy import prod, Poly
from sympy.abc import x
def A076634(n):
    y = Poly(prod(2*x+i for i in range(1,n+1))).all_coeffs()[::-1]
    return y.index(max(y)) # Chai Wah Wu, Mar 07 2021