A098695 a(n) = 2^(n(n-1)/2) * Product_{k=1..n} k!.

1, 1, 4, 96, 18432, 35389440, 815372697600, 263006617337856000, 1357366631815981301760000, 126095668058466123464363212800000, 234278891648287676839670388023623680000000

Offset: 0

Author

Ralf Stephan, Sep 22 2004

Keywords

• nonn

Comments

Equals the absolute values of the row sums of A156921. - Johannes W. Meijer, Feb 20 2009

Links

• C. Radoux, Déterminants de Hankel et théorème de Sylvester, Séminaire Lotharingien de Combinatoire, B28b (1992), 9 pp.

Programs

Maple

A098695 := proc(n): 2^(n*(n-1)/2) * product(k!, k=1..n) end: seq(A098695(n), n=0..10);  # Johannes W. Meijer, Nov 22 2012

PARI

a(n) = 2^(n*(n-1)/2) * prod(k=1, n, k!); \\ Michel Marcus, Dec 11 2016

Formula

a(n) = 2^(n(n-1)/2) * Product_{k=1..n} k!.

a(n) = A006125(n) * A000178(n).

a(n) ~ 2^(n^2/2 + 1/2)*exp(-3*n^2/4 - n + 1/12)*n^(n^2/2 + n + 5/12)*Pi^(n/2 + 1/2)/A, where A is the Glaisher-Kinkelin constant (A074962). - Ilya Gutkovskiy, Dec 11 2016

Extensions

a(0)=1 added, offset changed, and edited by Johannes W. Meijer, Feb 23 2009, Nov 22 2012