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

%I A076634 #13 Mar 07 2021 17:48:06
%S A076634 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,
%T A076634 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,
%U A076634 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
%N A076634 Coefficient of x^a(n) in (x+1/2)*(x+2/2)*...*(x+n/2) is the largest one.
%o A076634 (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
%o A076634 (Python)
%o A076634 from sympy import prod, Poly
%o A076634 from sympy.abc import x
%o A076634 def A076634(n):
%o A076634     y = Poly(prod(2*x+i for i in range(1,n+1))).all_coeffs()[::-1]
%o A076634     return y.index(max(y)) # _Chai Wah Wu_, Mar 07 2021
%Y A076634 Cf. A076620.
%K A076634 nonn
%O A076634 1,3
%A A076634 _Benoit Cloitre_, Nov 10 2002