The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A133413 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing all changes.

A133413

Half the number of ways of placing up to n^2 pawns on an n x n chessboard so that it balances at its midpoint.
(history; published version)

#7 by Alois P. Heinz at Sat Jan 07 19:01:41 EST 2023

STATUS

proposed

approved

#6 by Andrew Howroyd at Sat Jan 07 18:44:08 EST 2023

STATUS

editing

proposed

#5 by Andrew Howroyd at Sat Jan 07 17:10:12 EST 2023

DATA

1, 2, 24, 492, 202064, 100202536, 888531141152, 8548846756027594, 1400822035743239844640, 241149984205773848119833656, 691305758149247080625180837349904, 2048332087899166877612856148780183708362, 99840603982108483679316058344233421388081447648

PROG

(PARI) a(n) = {polcoef(polcoef(prod(j=1, n, prod(k=1, n, 1 + 'x^(2*k-n-1)*'y^(2*j-n-1) )), 0), 0)/2} \\ Andrew Howroyd, Jan 07 2023

CROSSREFS

Cf. A133406, A133414.

EXTENSIONS

a(12)-a(13) from Andrew Howroyd, Jan 07 2023

STATUS

approved

editing

#4 by Russ Cox at Sat Mar 31 12:35:06 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net), _, Nov 25 2007

Discussion

Sat Mar 31

12:35

OEIS Server: https://oeis.org/edit/global/875

#3 by N. J. A. Sloane at Sat Oct 02 03:00:00 EDT 2010

KEYWORD

nonn,new

nonn

AUTHOR

Ron R. H. Hardin (rhhardin(AT)att.net), Nov 25 2007

#2 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

KEYWORD

nonn,new

nonn

AUTHOR

Ron Hardin (rhhrhhardin(AT)cadenceatt.comnet), Nov 25 2007

#1 by N. J. A. Sloane at Sun Dec 09 03:00:00 EST 2007

NAME

Half the number of ways of placing up to n^2 pawns on an n x n chessboard so that it balances at its midpoint.

DATA

1, 2, 24, 492, 202064, 100202536, 888531141152, 8548846756027594, 1400822035743239844640, 241149984205773848119833656, 691305758149247080625180837349904

OFFSET

1,2

KEYWORD

nonn,new

AUTHOR

Ron Hardin (rhh(AT)cadence.com), Nov 25 2007

STATUS

approved