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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 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.)