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

0,2

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

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

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 *)

Crossrefs

Cf. A000217, A027480.

Sequence in context: A222652 A227624 A199643 * A173221 A375840 A082787

Adjacent sequences: A056920 A056921 A056922 * A056924 A056925 A056926

Keyword

nonn

Author

Robert G. Wilson v, Sep 09 2000

Status

approved