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%I #14 Feb 24 2020 20:33:37
%S 1,1,3,10,36,121,447,1699,6589,25914,103633,419421,1714463,7068285,
%T 29361629,122764876,516245009,2181957489,9264275600,39495666700,
%U 169000837410,725574719515,3124648750706,13493792787415,58422790497226,253547380435914,1102776319943605
%N Number of 4-ary plane multitrees with n edges.
%H Andrew Howroyd, <a href="/A246975/b246975.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)/4)} (-1)^j*binomial(k, i)*binomial(i, j)*binomial(n-i, k-i-1)*binomial(n-4*j-1, i-1)/k for n > 0. - _Andrew Howroyd_, Feb 24 2020
%o (PARI) a(n)={my(m=4); 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. A128720 (2-ary case), A246974 (3-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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