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A035521 Fifth column of triangle A035342; related to A035330. 1
0, 0, 0, 0, 1, 45, 1470, 43890, 1291815, 38710035, 1199167200, 38692476900, 1304976397725, 46070080281225, 1702810398539250, 65862570279255750, 2663551451057371875, 112503209942059311375, 4957166849516125744500 (list; graph; refs; listen; history; text; internal format)



a(n) = A035342(n,5).

a(n), n>=5, enumerates unordered n-vertex forests composed of five plane (ordered) increasingly labeled ternary (3-ary) trees. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.


Table of n, a(n) for n=1..19.


a(n) = n!*A035330(n-4)/(5!*2^(n-5)), n >= 5; E.g.f. ((x*c(x/2)*(1-2*x)^(-1/2))^5)/5!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.


a(6)=45 increasing ternary 5-forest with n=6 vertices: there are three such 5-forests (four one vertex trees together with any of the three different 2-vertex trees) each with binomial(6,2)= 15 increasing labelings. W. Lang, Sep 14 2007.


Cf. A000108, A035342, A035330.

Sequence in context: A027476 A062262 A137716 * A107399 A053112 A240686

Adjacent sequences:  A035518 A035519 A035520 * A035522 A035523 A035524




Wolfdieter Lang



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Last modified December 7 20:31 EST 2019. Contains 329849 sequences. (Running on oeis4.)