A335378 Number of ways to linearly order the components of a simple labeled graph on n nodes so that the label 1 is in the first component.

0, 1, 2, 9, 75, 1152, 34682, 2138198, 269883034, 68817253672, 35198146897560, 36032836311773232, 73789380474381388000, 302234317635238719436144, 2475886860241348605928934912, 40564851111492400113490251715664, 1329228293742222434273523342085983312, 87112291457022644126987794521680595912960

Offset

0,3

Links

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

Formula

E.g.f.: Integral [d/dx log(g(x))]/(1 - log(g(x))) dx, where g(x) is the e.g.f. for A006125.

Mathematica

nn = 16; g[x_] := Sum[2^Binomial[n, 2] x^n/n!, {n, 0, nn+1}]; Table[n!, {n, 0, nn + 1}] CoefficientList[Integrate[Series[D[Log[g[x]], x]/(1 - Log[g[x]]), {x, 0, nn}], x], x]

Crossrefs

Cf. A006125, A335356.

Sequence in context: A243054 A080638 A370259 * A232471 A357539 A277181

Adjacent sequences: A335375 A335376 A335377 * A335379 A335380 A335381

Keyword

nonn

Author

Geoffrey Critzer, Jun 04 2020

Status

approved