A197505 Exponential transform of A006125.

1, 1, 3, 15, 121, 1665, 43883, 2437423, 289320049, 71423435521, 35912764315347, 36427941634714575, 74226534887938021609, 303199273967377493113473, 2480131664037469755458069819, 40602053121132407513785975382767, 1329877926764331449042460153768864481

Offset

0,3

Comments

a(n) is the number of simple labeled graphs on n nodes where the nodes are divided into any number of groups and no edge connects nodes of different groups. (Nodes within a group are not necessarily connected).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Formula

E.g.f.: exp(A(x)-1) where A(x) = Sum_{n>=0} 2^C(n,2) x^n/n! is the e.g.f. of A006125.

Maple

a:= proc(n) option remember; `if`(n=0, 1,
      add(binomial(n-1, j-1) *2^(j*(j-1)/2) *a(n-j), j=1..n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Oct 16 2011

Mathematica

a=Sum[2^Binomial[n, 2] x^n/n!, {n, 0, 20}];  Range[0, 20]! CoefficientList[Series[Exp[a-1], {x, 0, 20}], x]

Crossrefs

Sequence in context: A156360 A160884 A173468 * A348903 A191371 A113077

Adjacent sequences: A197502 A197503 A197504 * A197506 A197507 A197508

Keyword

nonn

Author

Geoffrey Critzer, Oct 15 2011

Status

approved