The On-Line Encyclopedia of Integer Sequences (OEIS)

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A165343

First series of Hankel determinants based on A001044(n)=(n!)^2 : a(n)=det(A001044(i+j-2))=det(((i+j-2)!)^2), i,j=1,2...n. Hankel transform of A001044.
(history; published version)

#8 by Vaclav Kotesovec at Sun Feb 24 07:35:02 EST 2019

STATUS

editing

approved

#7 by Vaclav Kotesovec at Sun Feb 24 07:14:53 EST 2019

MATHEMATICA

nmax = 15; Table[Det[Table[((i+j-2)!)^2, {i, 1, k}, {j, 1, k}]], {k, 1, nmax}] (* Vaclav Kotesovec, Feb 24 2019 *)

STATUS

approved

editing

#6 by Michel Marcus at Sat May 13 12:42:09 EDT 2017

STATUS

reviewed

approved

#5 by Joerg Arndt at Sat May 13 12:07:12 EDT 2017

STATUS

proposed

reviewed

#4 by Eric Rowland at Sat May 13 11:58:51 EDT 2017

STATUS

editing

proposed

#3 by Eric Rowland at Sat May 13 11:57:57 EDT 2017

NAME

First series of Hankel determinants based on A001044(n)=(n!)^2 : a(n)=det(A001044(i+j-2))=det(((i+j-2)!)^2), i,j=1,2...n. Hankel transform of A05001044(n)A001044.

STATUS

approved

editing

Discussion

Sat May 13

11:58

Eric Rowland: Fix sequence number

#2 by Russ Cox at Fri Mar 30 18:49:55 EDT 2012

AUTHOR

_Karol A. Penson (penson(AT)lptl.jussieu.fr), _, Sep 15 2009

Discussion

Fri Mar 30

18:49

OEIS Server: https://oeis.org/edit/global/243

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

First series of Hankel determinants based on A001044(n)=(n!)^2 : a(n)=det(A001044(i+j-2))=det(((i+j-2)!)^2), i,j=1,2...n. Hankel transform of A05001044(n).

DATA

1, 3, 656, 58910976, 7213311014731776, 3024546589156405495726080000, 9172616430046109813423337553212211200000000

OFFSET

0,2

COMMENTS

It would be highly desirable to obtain a closed form for a(n).

KEYWORD

nonn

AUTHOR

Karol A. Penson (penson(AT)lptl.jussieu.fr), Sep 15 2009

STATUS

approved