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Number of strong triangulations of a fixed hexagon with n interior nodes.
3

%I #7 Mar 13 2021 17:02:20

%S 1,15,155,1410,12165,102548,856205,7128420,59386655,495973610,

%T 4156326090,34965061950,295326872685,2504471904060,21322339850120,

%U 182220932483936,1562911922345700,13451387178653575,116149864521206475,1006036370555080950,8739349976276626707,76128234963921173340

%N Number of strong triangulations of a fixed hexagon with n interior nodes.

%H Andrew Howroyd, <a href="/A341918/b341918.txt">Table of n, a(n) for n = 1..500</a>

%F a(n) = 120*(67*n^2 + 138*n + 68)*(4*n+7)!/((3*n+12)!*(n-1)!).

%o (PARI) a(n) = {120*(67*n^2 + 138*n + 68)*(4*n+7)!/((3*n+12)!*(n-1)!)}

%Y Column k=3 of A341856.

%K nonn

%O 1,2

%A _Andrew Howroyd_, Feb 23 2021