A077598 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.

0, 0, 2, 8, 15, 30, 43, 67, 90, 123, 149, 203, 237, 290, 343, 415, 464, 556, 613, 716, 800, 899, 972, 1126, 1218, 1342, 1458, 1616, 1716, 1916, 2026, 2215, 2365, 2540, 2690, 2959, 3098, 3300, 3485, 3762, 3919, 4221, 4388, 4667, 4921, 5179, 5364, 5762

Offset: 1

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Keywords

• nonn

Comments

These terms seem to be asymptotic to c*n^2*log(n) with c=0.69...

Examples

			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.
		

Crossrefs

Cf. A074586, A074587, A077596, A077597, A077599, A077600, A077601.

Programs

Mathematica

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 *)