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%I #15 Aug 05 2022 15:36:46
%S 1,2,3,10,25,161,721,5706,40881,385687,3628801,41268613,479001601,
%T 6324319717,87212177053,1317906346186,20922789888001,357099708702023,
%U 6402373705728001,121882752536893635,2432928081076384321,51140835669924352717
%N Row sums of absolute values of A182928.
%C The sum of multinomial coefficients can be computed recursively as
%C A005651(0) = 1 and A005651(n) = Sum_{1<=k<=n} binomial(n-1,k-1) * A182926(k) * A005651(n-k).
%C Möbius inversion yields: 1, 1, 2, 8, 24, 157, 720, 5696, 40878,...
%C A182927(2*i+1) = A182926(2*i+1).
%H Seiichi Manyama, <a href="/A182926/b182926.txt">Table of n, a(n) for n = 1..450</a>
%F a(n) = Sum_{d|n} n!/(d*((n/d)!)^d).
%F E.g.f.: Sum_{k>=1} log(1/(1 - x^k/k!)). - _Ilya Gutkovskiy_, May 21 2019
%e a(6) = 1 + 10 + 30 + 120 = 161.
%p A182926 := proc(n) local d;
%p add(n!/(d*((n/d)!)^d),d = numtheory[divisors](n)) end:
%p seq(A182926(i), i = 1..22);
%t a[n_] := Sum[ Abs[ -n!/(d*(-(n/d)!)^d)], {d, Divisors[n]}]; Table[ a[n], {n, 1, 22}] (* _Jean-François Alcover_, Jul 29 2013 *)
%Y Cf. A182927, A182928, A005651, A007837.
%K nonn
%O 1,2
%A _Peter Luschny_, Apr 16 2011
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