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A077596 Central coefficients of Moebius polynomials (A074586): coefficient of x^(n/2-1/2) if n is odd; coefficient of x^(n/2-1) if n is even and >4. The n-th Moebius polynomial, M(n,x), satisfies M(n,-1)=mu(n) the Moebius function of n.

%I A077596 #15 Feb 23 2015 22:10:39
%S A077596 1,2,4,8,15,30,57,108,206,393,752,1439,2772,5334,10327,19967,38808,
%T A077596 75319,146844,285862,558723,1090370,2135551,4176224,8193490,16050930,
%U A077596 31537017,61872863,121721157,239115024,470918888,926141652,1825708221
%N A077596 Central coefficients of Moebius polynomials (A074586): coefficient of x^(n/2-1/2) if n is odd; coefficient of x^(n/2-1) if n is even and >4. The n-th Moebius polynomial, M(n,x), satisfies M(n,-1)=mu(n) the Moebius function of n.
%C A077596 These terms seem to be asymptotic to c*2^n/sqrt(n) with c=1.2208..
%C A077596 c = 1.220916104316909855089768170983761594215082355524... . - _Vaclav Kotesovec_, Feb 11 2015
%e A077596 These are the largest coefficients of the Moebius polynomials, which begin:
%e A077596 M(1,x) = 1;
%e A077596 M(2,x) = 1 + 2x;
%e A077596 M(3,x) = 1 + 4x + 2x^2;
%e A077596 M(4,x) = 1 + 7x + 8x^2 + 2x^3;
%e A077596 M(5,x) = 1 + 9x +15x^2 +10x^3 + 2x^4;
%e A077596 M(6,x) = 1 +13x +30x^2 +27x^3 +12x^4 + 2x^5;
%e A077596 M(7,x) = 1 +15x +43x^2 +57x^3 +39x^4 +14x^5 + 2x^6;
%e A077596 M(8,x) = 1 +19x +67x^2+108x^3 +98x^4 +53x^5 +16x^6 + 2x^7; ...
%t A077596 m[n_, 1] = 1; m[n_, k_] := m[n, k] = Sum[Floor[n/j]*m[j, k - 1], {j, 1, n - 1}];
%t A077596 a[n_ /; n <= 4] := 2^(n - 1); a[n_?OddQ] := m[n, (n + 1)/2]; a[n_?EvenQ] := m[n, n/2]; Table[a[n], {n, 1, 33}] (* _Jean-François Alcover_, Jun 18 2013 *)
%Y A077596 Cf. A074586, A074587, A077597, A077598, A077599, A077600, A077601.
%K A077596 nonn
%O A077596 1,2
%A A077596 _Benoit Cloitre_ and _Paul D. Hanna_, Nov 10 2002