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%I #17 May 31 2018 10:38:10
%S 1,9,117,1785,29799,527085,9706503,184138713,3573805950,70625252863,
%T 1416298046436,28748759731965,589546754316126,12195537924351375,
%U 254184908607118800,5332692942907262361,112524941404978156215
%N Number of 9-ary trees.
%H S. Heubach, N. Y. Li and T. Mansour, <a href="https://doi.org/10.1016/j.disc.2007.11.012">Staircase tilings and k-Catalan structures</a>, Discrete Math., 308 (2008), 5954-5964.
%H J.-C. Novelli, J.-Y. Thibon, <a href="http://arxiv.org/abs/1403.5962">Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions</a>, arXiv preprint arXiv:1403.5962 [math.CO], 2014.
%F G.f. A(x) satisfies: A = x + A^9.
%F a(n) = C(k*n, n)/((k-1)*n+1), k=9.
%p with(combinat): for n from 1 to 40 do printf(`%d,`,binomial(9*n,n)/((9-1)*n+1)) od:
%Y Related algebraic sequences concerning trees: strictly k-ary trees (A000108: s=x+s^2, A001263: s=(x, y)+(x, s)+(s, y)+(s, s))), (A001764: s=x+s^3), (A002293: s=x+s^4), (A002294: s=x+s^5), (A002295: s=x+s^6), (A002296: s=x+s^7), (A007556: s=x+s^8), at most k-ary trees (A001006: s=x+xs+xs^2), (A036765-A036769, s=x+xs^2....+xs^k, k=3, 4, 5, 6, 7).
%K nonn
%O 0,2
%A Claude Lenormand (claude.lenormand(AT)free.fr), Mar 05 2001
%E More terms from _James A. Sellers_, Mar 15 2001
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