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 A277072 Number of n-node labeled graphs with one endpoint. 4
 0, 0, 0, 12, 320, 10890, 640836, 68362504, 13369203792, 4852623272670, 3314874720579180, 4318786169776866612, 10854838945689940034808, 53111101422881446287824390, 509319855642185873306564196780, 9619620856997967197817249800046480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES F. Harary and E. Palmer, Graphical Enumeration, (1973), p. 31, problem 1.16(a). LINKS Marko R. Riedel, Geoffrey Critzer, Math.Stackexchange.com, Proof of the closed form of the e.g.f. by combinatorial species. FORMULA E.g.f.: (z^2/(1-z))*(A'(z)-A(z)) where A(z) = exp(1/2*z^2) * Sum_{n>=0}(2^binomial(n, 2)*(z/exp(z))^n/n!). MAPLE MX := 16: XGF := exp(z^2/2)*add((z/exp(z))^n*2^binomial(n, 2)/n!, n=0..MX+5): K1 := z^2/(1-z)*(diff(XGF, z)-XGF): XS := series(K1, z=0, MX+1): seq(n!*coeff(XS, z, n), n=1..MX); MATHEMATICA m = 16; A[z_] := Exp[1/2*z^2]*Sum[2^Binomial[n, 2]*(z/Exp[z])^n/n!, {n, 0, m}]; egf = (z^2/(1 - z))*(A'[z] - A[z]); a[n_] := SeriesCoefficient[egf, {z, 0, n}]*n!; Array[a, m] (* Jean-François Alcover, Feb 23 2019 *) CROSSREFS Cf. A059167, A277073, A277074. Sequence in context: A341185 A279293 A180790 * A080325 A083431 A239781 Adjacent sequences:  A277069 A277070 A277071 * A277073 A277074 A277075 KEYWORD nonn AUTHOR Marko Riedel, Sep 27 2016 STATUS approved

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Last modified May 19 12:20 EDT 2022. Contains 353833 sequences. (Running on oeis4.)