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%I #11 Jun 18 2013 09:35:00
%S 0,0,2,8,15,30,43,67,90,123,149,203,237,290,343,415,464,556,613,716,
%T 800,899,972,1126,1218,1342,1458,1616,1716,1916,2026,2215,2365,2540,
%U 2690,2959,3098,3300,3485,3762,3919,4221,4388,4667,4921,5179,5364,5762
%N Coefficient of x^2 in the n-th Moebius polynomial (A074586), M(n,x), which satisfies M(n,-1)=mu(n) the Moebius function of n.
%C These terms seem to be asymptotic to c*n^2*log(n) with c=0.69...
%e These are the coefficients of x^2 in the Moebius polynomials, which begin: M(1,x)=1; M(2,x)=1 + 2x; M(3,x)=1 + 4x + 2x^2; M(4,x)=1 + 7x + 8x^2 + 2x^3; M(5,x)=1 + 9x +15x^2 +10x^3 + 2x^4; M(6,x)=1 +13x +30x^2 +27x^3 +12x^4 + 2x^5; M(7,x)=1 +15x +43x^2 +57x^3 +39x^4 +14x^5 + 2x^6; M(8,x)=1 +19x +67x^2+108x^3 +98x^4 +53x^5 +16x^6 + 2x^7.
%t m[n_, 1] = 1; m[n_, k_] := m[n, k] = Sum[Floor[n/j]*m[j, k - 1], {j, 1, n - 1}]; a[n_] := m[n, 3]; Table[a[n], {n, 1, 48}] (* _Jean-François Alcover_, Jun 18 2013 *)
%Y Cf. A074586, A074587, A077596, A077597, A077599, A077600, A077601.
%K nonn
%O 1,3
%A _Benoit Cloitre_ and _Paul D. Hanna_, Nov 10 2002
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