A375684 - OEIS

%I #8 Aug 24 2024 06:04:58

%S 1,0,-2,-3,16,90,-204,-4200,-5312,254016,1586160,-17970480,-294932736,

%T 790115040,54224747136,216483714720,-10481294822400,-137535688281600,

%U 1798183916660736,58769251106526720,-95282580797291520,-23811620975395061760,-203282679617698222080

%N Expansion of e.g.f. 1 / (1 - x * log(1 - x)).

%F a(0) = 1; a(n) = -n! * Sum_{k=2..n} 1/(k-1) * a(n-k)/(n-k)!.

%F a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k * k! * |Stirling1(n-k,k)|/(n-k)!.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*log(1-x))))

%o (PARI) a(n) = n!*sum(k=0, n\2, (-1)^k*k!*abs(stirling(n-k, k, 1))/(n-k)!);

%Y Cf. A052830, A367878, A367879.

%Y Cf. A375683.

%K sign

%O 0,3

%A _Seiichi Manyama_, Aug 24 2024