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URL: https://oeis.org/A054592

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A054592
Number of disconnected labeled graphs with n nodes.
15
0, 0, 1, 4, 26, 296, 6064, 230896, 16886864, 2423185664, 687883494016, 387139470010624, 432380088071584256, 959252253993204724736, 4231267540316814507357184, 37138269572860613284747227136, 649037449132671895468073434916864, 22596879313063804832510513481261154304
OFFSET
0,4
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
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