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%I #13 May 21 2019 05:53:36
%S 1,0,3,-8,25,-99,721,-5704,40881,-340325,3628801,-41245511,479001601,
%T -6129725315,87212177053,-1317906346184,20922789888001,
%U -354320889234597,6402373705728001,-121882630320799633,2432928081076384321,-51041048673495232715
%N Row sums of A182928.
%C The number of partitions of an n-set with distinct block sizes can
%C be computed recursively as A007837(0) = 1 and A007837(n) = - Sum_{1<=k<=n} binomial(n-1,k-1) * A182927(k) * A007837(n-k).
%C Möbius inversion yields: 1, -1, 2, -8, 24, -101, 720, -5696, 40878,...
%C A182927(2*i+1) = A182926(2*i+1)
%F a(n) = Sum_{d|n} -n!/(d*(-(n/d)!)^d).
%F E.g.f.: Sum_{k>=1} log(1 + x^k/k!). - _Ilya Gutkovskiy_, May 21 2019
%e a(6) = 1 - 10 + 30 - 120 = -99.
%p A182927 := proc(n) local d;
%p add(-n! / (d*(-(n/d)!)^d), d = numtheory[divisors](n)) end:
%p seq(A182927(i), i = 1..22);
%t a[n_] := Sum[ -n!/(d*(-(n/d)!)^d), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}] // Flatten (* _Jean-François Alcover_, Jul 29 2013 *)
%Y Cf. A182926, A182928, A005651, A007837.
%K sign
%O 1,3
%A _Peter Luschny_, Apr 16 2011