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.

1, 2, 4, 8, 15, 30, 57, 108, 206, 393, 752, 1439, 2772, 5334, 10327, 19967, 38808, 75319, 146844, 285862, 558723, 1090370, 2135551, 4176224, 8193490, 16050930, 31537017, 61872863, 121721157, 239115024, 470918888, 926141652, 1825708221

Offset: 1

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Keywords

• nonn

Comments

These terms seem to be asymptotic to c*2^n/sqrt(n) with c=1.2208..

c = 1.220916104316909855089768170983761594215082355524... . - Vaclav Kotesovec, Feb 11 2015

Examples

			These are the largest coefficients of 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, A077597, A077598, 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_ /; 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 *)