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A098695 a(n) = 2^(n(n-1)/2) * Prod_{k=1..n} k!. 3
1, 1, 4, 96, 18432, 35389440, 815372697600, 263006617337856000, 1357366631815981301760000, 126095668058466123464363212800000, 234278891648287676839670388023623680000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

LINKS

Table of n, a(n) for n=0..10.

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

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

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

PROG

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

CROSSREFS

Sequence in context: A203517 A146514 A181335 * A059201 A027638 A041275

Adjacent sequences:  A098692 A098693 A098694 * A098696 A098697 A098698

KEYWORD

nonn

AUTHOR

Ralf Stephan, Sep 22 2004

EXTENSIONS

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

STATUS

approved

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Last modified February 18 17:08 EST 2018. Contains 299325 sequences. (Running on oeis4.)