cp's OEIS Frontend

A356401 a(n) = n! * Sum_{k=1..n} Sum_{d|k} (-1)^(d+1)/(d * (k/d)!).

%I A356401 #9 Aug 05 2022 10:48:17
%S A356401 1,2,9,25,150,841,6608,41945,437986,4364741,51640952,526219585,
%T A356401 7319856206,102469338245,1671439939276,23909485105217,427384036676690,
%U A356401 7518024186420421,149244833247716000,2756811766466473601,61545779138627817622,1354007126970517958885
%N A356401 a(n) = n! * Sum_{k=1..n} Sum_{d|k} (-1)^(d+1)/(d * (k/d)!).
%F A356401 E.g.f.: -(1/(1-x)) * Sum_{k>0} (-1)^k * (exp(x^k) - 1)/k.
%F A356401 E.g.f.: (1/(1-x)) * Sum_{k>0} log(1+x^k)/k!.
%o A356401 (PARI) a(n) = n!*sum(k=1, n, sumdiv(k, d, (-1)^(d+1)/(d*(k/d)!)));
%o A356401 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(-sum(k=1, N, (-1)^k*(exp(x^k)-1)/k)/(1-x)))
%o A356401 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, log(1+x^k)/k!)/(1-x)))
%Y A356401 Cf. A356009, A356402.
%K A356401 nonn
%O A356401 1,2
%A A356401 _Seiichi Manyama_, Aug 05 2022