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A068337 a(n) = n!*Sum_{k=1..n} mu(k)/k, where mu(k) is the Möbius function. 4
1, 1, 1, 4, -4, 96, -48, -384, -3456, 328320, -17280, -207360, -481697280, -516741120, 79427174400, 1270834790400, 681401548800, 12265227878400, -6169334376038400, -123386687520768000, -158218429759488000, 47610136717000704000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..450

Friedrich Roesler, Riemann's hypothesis as an eigenvalue problem, Linear Algebra and its Applications, Vol. 81 (1986), pp. 153-198.

Friedrich Roesler, Riemann's hypothesis as an eigenvalue problem. II, Linear Algebra and its Applications, Vol. 92 (1987), pp. 45-73.

FORMULA

a(n) = (-1)^(n-1)*{determinant of the n X n matrix m(i,j) = i+(j (mod i))} - Benoit Cloitre, May 28 2004

From Amiram Eldar, Oct 22 2020: (Start)

a(n) = A000142(n)*A070888(n)/A070889(n).

a(n) ~ O(n! * n^(-1/2 + eps)), for every eps>0, if and only if Riemann's hypothesis is true (Roesler, 1986). (End)

MATHEMATICA

n = 25; Accumulate[Table[MoebiusMu[k]/k, {k, 1, n}]] * Range[n]! (* Amiram Eldar, Oct 22 2020 *)

CROSSREFS

Cf. A000142, A008683, A070888, A070889.

Sequence in context: A224092 A217188 A092209 * A009534 A009559 A163196

Adjacent sequences:  A068334 A068335 A068336 * A068338 A068339 A068340

KEYWORD

sign

AUTHOR

Leroy Quet, Feb 27 2002

STATUS

approved

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Last modified May 25 21:44 EDT 2022. Contains 354071 sequences. (Running on oeis4.)