A352013 a(n) = Sum_{d|n} (-1)^(n/d+1) * (n-1)!/(d-1)!.

1, 0, 3, -11, 25, -59, 721, -10919, 60481, -15119, 3628801, -93471839, 479001601, -8648639, 134399865601, -2833553923199, 20922789888001, -174888473759999, 6402373705728001, -228084898487846399, 3652732042831872001, -14079294028799

Offset: 1

Author

Seiichi Manyama, Feb 28 2022

Keywords

• sign

Links

• Robert Israel, Table of n, a(n) for n = 1..449

Crossrefs

Cf. A087906, A298906, A327243, A352014.

Programs

Maple

restart;
f:= proc(n) local d;
  add((-1)^(n/d + 1) * (n-1)!/(d-1)!, d = numtheory:-divisors(n))
end proc:
map(f, [$1..30]); # Robert Israel, Nov 14 2024

Mathematica

a[n_] := DivisorSum[n, (-1)^(n/#+1) * (n-1)!/(#-1)! &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *)

PARI

a(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)))

Formula

E.g.f.: Sum_{k>0} log(1+x^k)/k!.

E.g.f.: -Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k. - Seiichi Manyama, Jun 18 2023