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 A246974 Number of 3-ary plane multitrees with n edges. 2
 1, 1, 3, 10, 28, 93, 317, 1090, 3876, 13995, 51182, 189606, 709218, 2675230, 10166639, 38883721, 149559230, 578153160, 2245017535, 8752828951, 34250020397, 134465596581, 529509173245, 2090920335200, 8277633788511, 32846871639751, 130624556118075, 520512049658200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..200 M. Dziemianczuk, Enumerations of plane trees with multiple edges and Raney lattice paths, Discrete Mathematics 337 (2014): 9-24. FORMULA 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 PROG (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 CROSSREFS Cf. A002212, A128720 (2-ary case), A246975 (4-ary case). Sequence in context: A307063 A239885 A262251 * A278294 A260811 A108912 Adjacent sequences:  A246971 A246972 A246973 * A246975 A246976 A246977 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 14 2014 EXTENSIONS Terms a(11) and beyond from Andrew Howroyd, Feb 24 2020 STATUS approved

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Last modified January 25 05:31 EST 2021. Contains 340416 sequences. (Running on oeis4.)