A007834 Number of point labeled reduced 5-free two-graphs with n nodes.

1, 0, 1, 1, 16, 76, 1016, 10284, 157340, 2411756, 44953712, 899824256, 20283419872, 495216726096, 13202082981712, 378896535199888, 11690436112988224, 385173160930360192, 13509981115738946816

Offset

1,5

Links

Table of n, a(n) for n=1..19.

P. J. Cameron, Counting two-graphs related to trees, Elec. J. Combin., Vol. 2, #R4.

Formula

E.g.f.: -2*LambertW(-1/2*exp(-1/2)*(1+x)^(1/2))/(1+x). - Vladeta Jovovic, Aug 21 2006

a(n) ~ sqrt(2)*sqrt(4-exp(1)) * n^(n-1) / (8*exp(n-1)*(4*exp(-1)-1)^n). - Vaclav Kotesovec, Sep 30 2013

Mathematica

CoefficientList[Series[-2*LambertW[-1/2*E^(-1/2)*(1+x)^(1/2)]/(1+x), {x, 0, 15}], x]* Range[0, 15]! (* Vaclav Kotesovec, Sep 30 2013 *)

Crossrefs

Sequence in context: A118532 A253691 A300919 * A228741 A346636 A200873

Adjacent sequences: A007831 A007832 A007833 * A007835 A007836 A007837

Keyword

nonn

Author

Peter J. Cameron

Status

approved