A007746 Number of ways for n-3 nonintersecting loops to cross a line 2n times.

42, 640, 5894, 42840, 271240, 1569984, 8536890, 44346456, 222516030, 1086685600, 5193298110, 24384586200, 112831907760, 515709552000, 2332549535400, 10455495457248, 46500885666900, 205401168733824, 901819865269180, 3938266773556720, 17116175702216624

Offset

4,1

Links

Andrew Howroyd, Table of n, a(n) for n = 4..50

P. Di Francesco, O. Golinelli and E. Guitter, Meanders: a direct enumeration approach, Nucl. Phys. B 482 [ FS ] (1996) 497-535.

S. K. Lando and A. K. Zvonkin, Plane and projective meanders, Theoretical Computer Science Vol. 117, pp. 227-241, 1993.

Formula

a(n) = 4 * (2*n)! * (n^4+20*n^3+107*n^2-107*n+15) / ( 3*(n-4)! * (n+6)! ).

Mathematica

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 *)

Prog

(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

Crossrefs

A diagonal of triangle A008828.

Sequence in context: A104901 A091962 A269659 * A200853 A214945 A159947

Adjacent sequences: A007743 A007744 A007745 * A007747 A007748 A007749

Keyword

nonn

Author

Philippe Di Francesco (philippe(AT)amoco.saclay.cea.fr)

Status

approved