%I #20 Feb 24 2023 16:27:57

%S 0,0,1,4,26,296,6064,230896,16886864,2423185664,687883494016,

%T 387139470010624,432380088071584256,959252253993204724736,

%U 4231267540316814507357184,37138269572860613284747227136,649037449132671895468073434916864,22596879313063804832510513481261154304

%N Number of disconnected labeled graphs with n nodes.

%F a(n) = 2^binomial(n, 2) - A001187(n).

%F a(n) = n!*[x^n](g - log(g) - 1) where g = Sum_{n>=0} 2^binomial(n, 2) * x^n / n!. - _Geoffrey Critzer_, Nov 11 2011

%F a(n) = Sum_{k=0..n-1} A360604(n, k) * A001187(k). - _Peter Luschny_, Feb 24 2023

%p upto := 18: g := add(2^binomial(n, 2) * x^n / n!, n = 0..upto+1):

%p ser := series(g - log(g) - 1, x, upto+1):

%p seq(n!*coeff(ser, x, n), n = 0..upto); # _Peter Luschny_, Feb 24 2023

%t g=Sum[2^Binomial[n,2]x^n/n!,{n,0,20}]; Range[0,20]! CoefficientList[Series[g-Log[g]-1,{x,0,20}],x] (* _Geoffrey Critzer_, Nov 11 2011 *)

%Y Cf. A001187, A000719, A360604.

%K easy,nonn

%O 0,4

%A _Vladeta Jovovic_, Apr 15 2000

%E Edited and extended with a(0) = 0 by _Peter Luschny_, Feb 24 2023