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%I #7 Jan 07 2023 19:01:41
%S 1,2,24,492,202064,100202536,888531141152,8548846756027594,
%T 1400822035743239844640,241149984205773848119833656,
%U 691305758149247080625180837349904,2048332087899166877612856148780183708362,99840603982108483679316058344233421388081447648
%N 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.
%o (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
%Y Cf. A133406, A133414.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 25 2007
%E a(12)-a(13) from _Andrew Howroyd_, Jan 07 2023
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