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A275462 Number of leaves in all simple labeled connected graphs on n nodes. 0
0, 0, 2, 6, 48, 760, 21840, 1121568, 104510336, 18111498624, 5966666196480, 3794613745429760, 4704698796461841408, 11443317008255593064448, 54831540882238864189229056, 519046250316393184411087165440, 9726643425055315256306341282775040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A leaf is a vertex of degree 1.

LINKS

Table of n, a(n) for n=0..16.

FORMULA

E.g.f.: x*A(x) = x^2* d[log(B(x))]/dx where A(x) is the e.g.f. for A053549 and B(x) is the e.g.f. for A006125.

For n>=1, a(n) = n*(n-1)*A001187(n-1).

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, 2^(n*(n-1)/2)-

      add(k*binomial(n, k)* 2^((n-k)*(n-k-1)/2)*b(k), k=1..n-1)/n)

    end:

a:= n-> n*(n-1)*b(n-1):

seq(a(n), n=0..20);  # Alois P. Heinz, Jul 31 2016

MATHEMATICA

nn = 15; Clear[f]; f[z_] := Sum[2^Binomial[n, 2] z^n/n!, {n, 0, nn + 1}]; Range[0, nn]! CoefficientList[Series[ z z D[Log[f[z]], z] , {z, 0, nn}], z]

CROSSREFS

Cf. A095338.

Sequence in context: A129464 A003053 A113296 * A063744 A141609 A096313

Adjacent sequences:  A275459 A275460 A275461 * A275463 A275464 A275465

KEYWORD

nonn

AUTHOR

Geoffrey Critzer, Jul 28 2016

STATUS

approved

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Last modified February 21 04:55 EST 2020. Contains 332086 sequences. (Running on oeis4.)