A059967 Number of 9-ary trees.

1, 9, 117, 1785, 29799, 527085, 9706503, 184138713, 3573805950, 70625252863, 1416298046436, 28748759731965, 589546754316126, 12195537924351375, 254184908607118800, 5332692942907262361, 112524941404978156215

Offset: 0

Author

Claude Lenormand (claude.lenormand(AT)free.fr), Mar 05 2001

Keywords

• nonn

Links

• S. Heubach, N. Y. Li and T. Mansour, Staircase tilings and k-Catalan structures, Discrete Math., 308 (2008), 5954-5964.
• J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations,(m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014.

Crossrefs

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).

Programs

Maple

with(combinat): for n from 1 to 40 do printf(`%d,`,binomial(9*n,n)/((9-1)*n+1)) od:

Formula

G.f. A(x) satisfies: A = x + A^9.

a(n) = C(k*n, n)/((k-1)*n+1), k=9.

Extensions

More terms from James Sellers, Mar 15 2001