This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A033277 #15 Jul 08 2025 19:50:02 %S A033277 0,42,330,1485,5005,14014,34398,76440,157080,302940,554268,969969, %T A033277 1633905,2662660,4214980,6503112,9806280,14486550,21007350,29954925, %U A033277 42063021,58241106,79606450,107520400,143629200,189909720,248720472,322858305,415621185,530877480 %N A033277 Number of diagonal dissections of an n-gon into 5 regions. %C A033277 Number of standard tableaux of shape (n-5,2,2,2,2) (n>=7). - _Emeric Deutsch_, May 20 2004 %C A033277 Number of short bushes with n+3 edges and 5 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(7)=42 because the only short bushes with 10 edges and 5 branch nodes are the fortytwo full binary trees with 10 edges. Column 5 of A108263. - _Emeric Deutsch_, May 29 2005 %H A033277 D. Beckwith, <a href="http://www.jstor.org/stable/2589081">Legendre polynomials and polygon dissections?</a>, Amer. Math. Monthly, 105 (1998), 256-257. %H A033277 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 A033277 a(n) = binomial(n+3, 4)*binomial(n-3, 4)/5. %F A033277 G.f.: z^7(42-48z+27z^2-8z^3+z^4)/(1-z)^9. - _Emeric Deutsch_, May 29 2005 %o A033277 (PARI) vector(40, n, n+=5; binomial(n+3, 4)*binomial(n-3, 4)/5) \\ _Michel Marcus_, Jun 18 2015 %Y A033277 Cf. A108263. %K A033277 nonn %O A033277 6,2 %A A033277 _N. J. A. Sloane_