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A033278 Number of diagonal dissections of an n-gon into 6 regions.

%I A033278 #15 Jul 08 2025 19:50:09
%S A033278 0,132,1287,7007,28028,91728,259896,659736,1534896,3325608,6789783,
%T A033278 13180167,24496472,43835792,75869640,127481640,208606320,333316620,
%U A033278 521215695,799197399,1203649524,1783184480,2601993680,3743934480,5317472160,7461614160,10352989647
%N A033278 Number of diagonal dissections of an n-gon into 6 regions.
%C A033278 Number of standard tableaux of shape (n-6,2,2,2,2,2) (n>=8). - _Emeric Deutsch_, May 20 2004
%C A033278 Number of short bushes with n+4 edges and 6 branch nodes (i. e. nodes with outdegree at least 2; a short bush is an ordered tree with no nodes of outdegree 1). Example: a(8)=132 because the only short bushes with 12 edges and 6 branch nodes are the one-hundred-thirty-two full binary trees with 12 edges. Column 6 of A108263. - _Emeric Deutsch_, May 29 2005
%H A033278 T. D. Noe, <a href="/A033278/b033278.txt">Table of n, a(n) for n = 7..1000</a>
%H A033278 D. Beckwith, <a href="http://www.jstor.org/stable/2589081">Legendre polynomials and polygon dissections?</a>, Amer. Math. Monthly, 105 (1998), 256-257.
%H A033278 F. R. Bernhart, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00054-0">Catalan, Motzkin and Riordan numbers</a>, Discr. Math., 204 (1999), 73-112.
%F A033278 a(n) = binomial(n+4, 5)*binomial(n-3, 5)/6.
%F A033278 G.f.: z^8(132-165z+110z^2-44z^3+10z^4-z^5)/(1-z)^11. - _Emeric Deutsch_, May 29 2005
%o A033278 (PARI) vector(40, n, n+=6; binomial(n+4, 5)*binomial(n-3, 5)/6) \\ _Michel Marcus_, Jun 18 2015
%Y A033278 Cf. A108263.
%K A033278 nonn
%O A033278 7,2
%A A033278 _N. J. A. Sloane_