This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A245012 The number of labeled caterpillar graphs on n nodes. 0
 1, 1, 1, 3, 16, 125, 1296, 15967, 225184, 3573369, 63006400, 1222037531, 25856693424, 592684459237, 14630486811136, 386952126342615, 10916525199478336, 327220530559545713, 10385328804324011136, 347921328910693707955, 12269256633867840769360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS All trees of order less than 7 are caterpillars so for 0 < n < 7, a(n) = n^(n-2) = A000272(n). Call a rooted labeled tree of height at most one a short tree.  A caterpillar is a single short tree or a succession of short trees sandwiched between two nontrivial short trees. - Geoffrey Critzer, Aug 03 2016 LINKS Eric Weisstein's World of Mathematics, Caterpillar FORMULA E.g.f.: C(x) - x^2/2! + x + 1 + Sum_{k>=0} A(x)^k*C(x)^2/2, where A(x) = x*exp(x) and C(x) = A(x) - x. EXAMPLE a(7) = 15967 because there is only one unlabeled tree that is not a caterpillar (Cf. A052471): o-o-o-o-o     |     o     |     o This tree has 840 labelings. So 7^5 - 840 = 15967. MATHEMATICA nn=20; a=x Exp[x]; c=a-x; Range[0, nn]!CoefficientList[Series[c-x^2/2!+x+1+Sum[a^k c^2/2, {k, 0, nn}], {x, 0, nn}], x] PROG (PARI) N=33;  x='x+O('x^N); A = x *exp(x);  C = A - x; egf = C - x^2/2! + x + 1 + sum(k=0, N, A^k*C^2/2); Vec(serlaplace(egf)) \\ Joerg Arndt, Jul 10 2014 CROSSREFS Cf. A005418. Sequence in context: A157457 A000950 A320254 * A000951 A000272 A246527 Adjacent sequences:  A245009 A245010 A245011 * A245013 A245014 A245015 KEYWORD nonn AUTHOR Geoffrey Critzer, Jul 09 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 15:15 EDT 2019. Contains 328267 sequences. (Running on oeis4.)