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

%I A352013 #26 Nov 14 2024 02:11:03
%S A352013 1,0,3,-11,25,-59,721,-10919,60481,-15119,3628801,-93471839,479001601,
%T A352013 -8648639,134399865601,-2833553923199,20922789888001,-174888473759999,
%U A352013 6402373705728001,-228084898487846399,3652732042831872001,-14079294028799
%N A352013 a(n) = Sum_{d|n} (-1)^(n/d+1) * (n-1)!/(d-1)!.
%H A352013 Robert Israel, <a href="/A352013/b352013.txt">Table of n, a(n) for n = 1..449</a>
%F A352013 E.g.f.: Sum_{k>0} log(1+x^k)/k!.
%F A352013 E.g.f.: -Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k. - _Seiichi Manyama_, Jun 18 2023
%p A352013 restart;
%p A352013 f:= proc(n) local d;
%p A352013   add((-1)^(n/d + 1) * (n-1)!/(d-1)!, d = numtheory:-divisors(n))
%p A352013 end proc:
%p A352013 map(f, [$1..30]); # _Robert Israel_, Nov 14 2024
%t A352013 a[n_] := DivisorSum[n, (-1)^(n/#+1) * (n-1)!/(#-1)! &]; Array[a, 22] (* _Amiram Eldar_, Aug 30 2023 *)
%o A352013 (PARI) a(n) = sumdiv(n, d, (-1)^(n/d+1)*(n-1)!/(d-1)!);
%o A352013 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)))
%Y A352013 Cf. A087906, A298906, A327243, A352014.
%K A352013 sign
%O A352013 1,3
%A A352013 _Seiichi Manyama_, Feb 28 2022