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%I #14 Feb 08 2022 12:13:06
%S 1,5,20,85,385,1836,9120,46805,246675,1328925,7292688,40652780,
%T 229698220,1313175880,7585060680,44212723797,259808593975,
%U 1537840085775,9162371040900,54913015836525,330888232445505,2003659057873200,12187811305300800,74444226847892460,456458831442283860
%N Number of simple strong triangulations of a fixed pentagon with n interior nodes.
%H Andrew Howroyd, <a href="/A341920/b341920.txt">Table of n, a(n) for n = 1..500</a>
%F From _Peter Bala_, Feb 06 2022: (Start)
%F Conjectures:
%F a(n) = 5*(5*n-3)*binomial(3*n,n)/((n+1)*(2*n+1)*(2*n+3)).
%F a(n+1) = 3*(3*n+1)*(3*n+2)*(5*n+2)/(2*(n+2)*(2*n+5)*(5*n-3))*a(n). (End)
%o (PARI) R(25,2) \\ R defined in A210664.
%Y Row m = 2 of A210664.
%Y Cf. A000256, A341917.
%K nonn
%O 1,2
%A _Andrew Howroyd_, Feb 24 2021
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