A056923 Write the integers in groups: 0; 1,2; 3,4,5; 6,7,8,9; ... and form the product of the members of each group.

0, 2, 60, 3024, 240240, 27907200, 4475671200, 948964262400, 257256702743040, 86839771951296000, 35728290125079552000, 17602963463032472448000, 10233395250958706770944000, 6932022668773077815267328000

Offset: 0

Author

Robert G. Wilson v, Sep 09 2000

Keywords

• nonn

Comments

Each group begins with a triangular number and proceeds until one short of the next triangular number.

Also, the number under the radical using Brahmagupta's formula for an n-sided cyclic quadrilateral with sides 1..n. - Ben Paul Thurston, Dec 05 2006

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Nick Hobson, Solution to puzzle 10: Farmer's enclosure

Crossrefs

Cf. A000217, A027480.

Programs

Maple

a:= n-> mul(n*(n+1)/2+j, j=0..n):
seq(a(n), n=0..15);  # Alois P. Heinz, Feb 02 2019

Mathematica

Table[(n (n + 3)/2)!/((n - 1)(n + 2)/2)!, {n, 0, 15}]
Times@@Range[First[#],Last[#]-1]&/@Partition[Accumulate[Range[0,15]],2,1] (* Harvey P. Dale, Apr 25 2014 *)

Formula

a(n) = (n (n + 3)/2)!/((n - 1)(n + 2)/2)!.

a(n) = Product_{j=1..n+1} ((n+2)*(n+1)/2-j). - Ben Paul Thurston, Dec 05 2006