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%I #52 Aug 19 2022 06:04:58
%S 1,11,84,520,2835,14133,65960,292536,1245789,5132375,20569512,
%T 80541300,309143065,1166302239,4334300976,15895046840,57608669274,
%U 206606077758,733992204988,2585415612500,9036556157100,31362262768684,108144498780096,370700681812032
%N a(n) is 1/5 times the number of anti-chains of size four in "0,1,2" Motzkin trees on n edges.
%C See A335355 for details.
%H Lifoma Salaam, <a href="https://search.proquest.com/docview/193997569">Combinatorial statistics on phylogenetic trees</a>, Ph.D. Dissertation, Howard University, Washington D.C., 2008; see Definition 42 (p. 30), Theorem 44 (p. 33), and Table 2.4 (p. 39).
%F a(n) = A335355(n)/5.
%F D-finite with recurrence -(n+2)*(n-6)*a(n) +(n+2)*(4*n-17)*a(n-1) +(2*n^2-n-90)*a(n-2) -3*(n+2)*(4*n-3)*a(n-3) -9*(n+2)*(n+1)*a(n-4)=0. - _R. J. Mathar_, Aug 19 2022
%o (PARI) default(seriesprecision, 50);
%o M(z) = (1 - z - sqrt(1 - 2*z - 3*z^2))/(2*z^2); /* g.f. of A001006 */
%o T(z) = 1/sqrt(1 - 2*z - 3*z^2); /* g.f. of A002426 */
%o for(n=0, 30, print1(polcoef(z^6*T(z)^7*M(z)^4, n, z), ", "))
%Y Cf. A001006, A002426, A335355.
%K nonn
%O 6,2
%A _Petros Hadjicostas_, Jun 08 2020
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