A054592 Number of disconnected labeled graphs with n nodes.

0, 0, 1, 4, 26, 296, 6064, 230896, 16886864, 2423185664, 687883494016, 387139470010624, 432380088071584256, 959252253993204724736, 4231267540316814507357184, 37138269572860613284747227136, 649037449132671895468073434916864, 22596879313063804832510513481261154304

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Formula

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

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

a(n) = Sum_{k=0..n-1} A360604(n, k) * A001187(k). - Peter Luschny, Feb 24 2023

Maple

upto := 18: g := add(2^binomial(n, 2) * x^n / n!, n = 0..upto+1):
ser := series(g - log(g) - 1, x, upto+1):
seq(n!*coeff(ser, x, n), n = 0..upto); # Peter Luschny, Feb 24 2023

Mathematica

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 *)

Crossrefs

Cf. A001187, A000719, A360604.

Sequence in context: A304864 A167811 A156306 * A357795 A102202 A271613

Adjacent sequences: A054589 A054590 A054591 * A054593 A054594 A054595

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 15 2000

Extensions

Edited and extended with a(0) = 0 by Peter Luschny, Feb 24 2023

Status

approved