cp's OEIS Frontend

A275462 Number of leaves in all simple labeled connected graphs on n nodes.

%I A275462 #12 Aug 01 2016 08:36:17
%S A275462 0,0,2,6,48,760,21840,1121568,104510336,18111498624,5966666196480,
%T A275462 3794613745429760,4704698796461841408,11443317008255593064448,
%U A275462 54831540882238864189229056,519046250316393184411087165440,9726643425055315256306341282775040
%N A275462 Number of leaves in all simple labeled connected graphs on n nodes.
%C A275462 A leaf is a vertex of degree 1.
%F A275462 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.
%F A275462 For n>=1, a(n) = n*(n-1)*A001187(n-1).
%p A275462 b:= proc(n) option remember; `if`(n=0, 1, 2^(n*(n-1)/2)-
%p A275462       add(k*binomial(n, k)* 2^((n-k)*(n-k-1)/2)*b(k), k=1..n-1)/n)
%p A275462     end:
%p A275462 a:= n-> n*(n-1)*b(n-1):
%p A275462 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jul 31 2016
%t A275462 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]
%Y A275462 Cf. A095338.
%K A275462 nonn
%O A275462 0,3
%A A275462 _Geoffrey Critzer_, Jul 28 2016