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%I #21 Sep 08 2022 08:44:35
%S 42,640,5894,42840,271240,1569984,8536890,44346456,222516030,
%T 1086685600,5193298110,24384586200,112831907760,515709552000,
%U 2332549535400,10455495457248,46500885666900,205401168733824,901819865269180,3938266773556720,17116175702216624
%N Number of ways for n-3 nonintersecting loops to cross a line 2n times.
%H Andrew Howroyd, <a href="/A007746/b007746.txt">Table of n, a(n) for n = 4..50</a>
%H P. Di Francesco, O. Golinelli and E. Guitter, <a href="http://arXiv.org/abs/hep-th/9607039">Meanders: a direct enumeration approach</a>, Nucl. Phys. B 482 [ FS ] (1996) 497-535.
%H S. K. Lando and A. K. Zvonkin, <a href="http://dx.doi.org/10.1016/0304-3975(93)90316-L">Plane and projective meanders</a>, Theoretical Computer Science Vol. 117, pp. 227-241, 1993.
%F a(n) = 4 * (2*n)! * (n^4+20*n^3+107*n^2-107*n+15) / ( 3*(n-4)! * (n+6)! ).
%t Table[4 (2 n)!/(3 (n - 4)! (n+6)!) (n^4 + 20 n^3 + 107 n^2 - 107 n + 15), {n, 4, 30}] (* _Vincenzo Librandi_, Nov 23 2015 *)
%o (Magma) [4*Factorial(2*n)/(3*Factorial(n-4)*Factorial(n+6))* (n^4+20*n^3+107*n^2-107*n+15): n in [4..25]]; // _Vincenzo Librandi_, Nov 23 2015
%Y A diagonal of triangle A008828.
%K nonn
%O 4,1
%A Philippe Di Francesco (philippe(AT)amoco.saclay.cea.fr)
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