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A197505 Exponential transform of A006125. 2
1, 1, 3, 15, 121, 1665, 43883, 2437423, 289320049, 71423435521, 35912764315347, 36427941634714575, 74226534887938021609, 303199273967377493113473, 2480131664037469755458069819, 40602053121132407513785975382767, 1329877926764331449042460153768864481 (list; graph; refs; listen; history; text; internal format)
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 * A191371 A113077 A251661

Adjacent sequences:  A197502 A197503 A197504 * A197506 A197507 A197508

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Oct 15 2011

STATUS

approved

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Last modified June 24 05:39 EDT 2019. Contains 324318 sequences. (Running on oeis4.)