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A282734 Number of triangulations of a convex 5-gon in the plane each of whose sides is subdivided by n points. 1

%I

%S 5,250,13740,699310,33138675,1484701075,63681535780,2639190848280,

%T 106403568809545,4194330516135610,162275686298727710,

%U 6180361117463387590,232249233257266145145,8627435520542763854065,317285140062014506979360,11566298576075812803892160

%N Number of triangulations of a convex 5-gon in the plane each of whose sides is subdivided by n points.

%H Lars Blomberg, <a href="/A282734/b282734.txt">Table of n, a(n) for n = 0..99</a>

%H Andrei Asinowski, Christian Krattenthaler, Toufik Mansour, <a href="http://arxiv.org/abs/1604.02870">Counting triangulations of some classes of subdivided convex polygons</a>, arXiv:1604.02870 [math.CO], 2016.

%F From Asinowski and Krattenthaler equation 2.7: a(n) = tr(5,n+1). - _Lars Blomberg_, Mar 04 2017

%t tr[k_, r_] := Sum[(-1)^j 2^l Binomial[k, j] Binomial[k-2+l, l] Binomial[ (r-1)k-l-3, r k - (r+1)j-l-2], {j, 0, k}, {l, 0, r k - (r+1)j - 2}];

%t a[n_] := tr[5, n+1];

%t Table[a[n], {n, 0, 15}] (* _Jean-Fran├žois Alcover_, Oct 10 2018 *)

%K nonn

%O 0,1

%A _N. J. A. Sloane_, Mar 03 2017

%E More terms from _Lars Blomberg_, Mar 04 2017

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Last modified August 4 16:34 EDT 2020. Contains 336202 sequences. (Running on oeis4.)