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%I #14 Feb 24 2020 20:33:12
%S 1,1,3,10,28,93,317,1090,3876,13995,51182,189606,709218,2675230,
%T 10166639,38883721,149559230,578153160,2245017535,8752828951,
%U 34250020397,134465596581,529509173245,2090920335200,8277633788511,32846871639751,130624556118075,520512049658200
%N Number of 3-ary plane multitrees with n edges.
%C A k-ary plane multitree is a plane tree with edges having multiplicity and the outdegree of any node does not exceed k. The number of plane multitrees with n edges (without restriction on outdegree) is given by A002212(n). - _Andrew Howroyd_, Feb 24 2020
%H Andrew Howroyd, <a href="/A246974/b246974.txt">Table of n, a(n) for n = 0..200</a>
%H M. Dziemianczuk, <a href="http://dx.doi.org/10.1016/j.disc.2014.07.024">Enumerations of plane trees with multiple edges and Raney lattice paths</a>, Discrete Mathematics 337 (2014): 9-24.
%F a(n) = Sum_{k=1..n+1} Sum_{i=1..k-1} Sum_{j=0..floor((n-i)/3)} (-1)^j*binomial(k, i)*binomial(i, j)*binomial(n-i, k-i-1)*binomial(n-3*j-1, i-1)/k for n > 0. - _Andrew Howroyd_, Feb 24 2020
%o (PARI) a(n)={my(m=3); if(n<1, n==0, sum(k=1, n+1, sum(i=1, k-1, sum(j=0, (n-i)\m, (-1)^j*binomial(k, i)*binomial(i, j)*binomial(n-i, k-i-1)*binomial(n-m*j-1, i-1)))/k))} \\ _Andrew Howroyd_, Feb 24 2020
%Y Cf. A002212, A128720 (2-ary case), A246975 (4-ary case).
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Sep 14 2014
%E Terms a(11) and beyond from _Andrew Howroyd_, Feb 24 2020
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