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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. 6
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified August 14 15:36 EDT 2024. Contains 375165 sequences. (Running on oeis4.)