A318600 a(1) = 1; a(n+1) = Sum_{d|n} (-1)^(n/d+1)*d*a(d).

1, 1, 1, 4, 13, 66, 394, 2759, 22053, 198481, 1984746, 21832207, 261986098, 3405819275, 47681467093, 715222006464, 11443552081333, 194540385382662, 3501726936689833, 66532811797106828, 1330656235940151698, 27943780954743188420, 614763181004328313035, 14139553163099551199806

Offset: 1

Author

Ilya Gutkovskiy, Aug 29 2018

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A004111, A157311, A318372.

Programs

Maple

f:= proc(n) option remember;
add((-1)^((n-1)/d+1)*d*procname(d), d = numtheory:-divisors(n-1))
end proc:
f(1):= 1:
map(f, [$1..30]); # Robert Israel, Aug 30 2018

Mathematica

a[1] = 1; a[n_] := a[n] = Sum[(-1)^((n - 1)/d + 1) d a[d] , {d, Divisors[n - 1]}]; Table[a[n], {n, 24}]

Formula

L.g.f.: log(Product_{n>=1} (1 + x^n)^a(n)) = Sum_{n>=1} a(n+1)*x^n/n.