%I #5 Jan 29 2023 21:02:30

%S 1,1,6,53,647,10092,191915,4309769,111682044,3281731611,107860953795,

%T 3921762633846,156322429050397,6779458454252941,317841794915501862,

%U 16020304439710056785,863955306007083830051,49641711131738762890764,3027776406780183894833791,195382900651186641677702197

%N a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!) * [x^n] (1 - exp(-LambertW(x*exp(-x))))^k.

%F a(n) = Sum_{k=0..n} |A360176(n, k)|.

%p egf := k -> (1 - exp(-LambertW(x*exp(-x))))^k / k!:

%p ser := k -> series(egf(k), x, 22):

%p T := (n, k) -> (-1)^(n-k)*n!*coeff(ser(k), x, n):

%p seq(add(T(n, k), k = 0..n), n = 0..19);

%Y Cf. A360176.

%K nonn

%O 0,3

%A _Peter Luschny_, Jan 29 2023