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

1,2

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

Links

Table of n, a(n) for n=1..33.

Example

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; ...

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 *)

Crossrefs

Cf. A074586, A074587, A077597, A077598, A077599, A077600, A077601.

Sequence in context: A034338 A166861 A026023 * A091865 A065494 A134044

Adjacent sequences: A077593 A077594 A077595 * A077597 A077598 A077599

Keyword

nonn

Author

Benoit Cloitre and Paul D. Hanna, Nov 10 2002

Status

approved