A120445 Number of different convex inscribed polygons with n pair of sides of lengths d1, d2, ..., dn all distinct. Or number of bracelets with n pairs of beads, each pair of one among n colors.

1, 2, 11, 171, 5736, 312240, 24327000, 2554072920, 347351195520, 59397023589120, 12473374574505600, 3155763762320400000, 946729128624509260800, 332301924146113021900800, 134914581203304233287756800, 62735280259536165098353536000, 33124227977035089658775531520000

Offset: 1

Author

Ignacio Larrosa Cañestro, Jul 19 2006

Keywords

• nonn

Examples

			a(2) = 2 because there are two quadrilaterals with sides {1, 1, 2, 2}: a kite and a rectangle.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..235
• Ignacio Larrosa Cañestro, Marko Riedel, n-digonos.
• Marko Riedel, Pairs of beads on a ring.

Programs

Magma

[(Factorial(2*n)/2^n+(n+1)*Factorial(n)+n*Factorial(n))/(4*n): n in [1..20]]; // Vincenzo Librandi, Nov 22 2016

Mathematica

Table[((2 n)! / 2^n + (n + 1) n! + n n!) / (4 n), {n, 20}] (* Vincenzo Librandi, Nov 22 2016 *)

PARI

for(n=1,25, print1(((2*n)!/2^n + (2*n+1)*n!)/(4*n), ", ")) \\ G. C. Greubel, May 25 2017

Formula

a(n) = ((2n)!/2^n + (2n+1)*n!)/(4n).

a(n) ~ sqrt(Pi)*2^n*n^(2*n-1/2)/(2*exp(2*n)). - Ilya Gutkovskiy, Nov 21 2016

Extensions

Name clarified by Marko Riedel, Nov 22 2016