A182146 The number of simple labeled graphs on n nodes with no components of size 1 or 2.

1, 2, 4, 26, 296, 5904, 225576, 16673252, 2410709536, 686706538432, 386940976402960, 432315602878003448, 959210666655240937120, 4231214210938514819918144, 37138134131400012001269996000, 649036769087148274525770997003248, 22596872562588017123584720776207222528

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..80

Formula

E.g.f.: G(x)-G(x)/(exp(x)*exp(x^2/2)) where G(x) is the e.g.f. for A006125.

Example

a(4) = 26 because we have: * * * *; * * *-* times 6 labelings; *-*-* * times 12 labelings; *-* *-* times 3 labelings; and the complete graph on three nodes union with an isolated node which has 4 labelings. 1+6+12+3+4 = 26.

Mathematica

nn = 17; g = Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn}]; Drop[Range[0, nn]! CoefficientList[Series[g - g/(Exp[x] Exp[x^2/2]), {x, 0, nn}], x], 1]

Crossrefs

Sequence in context: A262067 A193480 A032076 * A218077 A240040 A088888

Adjacent sequences: A182143 A182144 A182145 * A182147 A182148 A182149

Keyword

nonn

Author

Geoffrey Critzer, Apr 14 2012

Status

approved