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.

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

Offset: 1

Author

R. H. Hardin, Nov 25 2007

Keywords

• nonn

Crossrefs

Cf. A133406, A133414.

Programs

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

Extensions

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