%I A063075
%S A063075 1,2,8,48,390,3656,37834,417540,4836452,58130756,719541996,9121965276,
%T A063075 117959864244,1551101290792,20689450250926,279395018584860,
%U A063075 3813887739881184,52557835511244660,730403326965323706
%N A063075 Number of partitions of 2n^2 whose Ferrers-plot fits within a 2n X 2n 
               box and cover an n X n box; number of ways to cut a 2n X 2n chessboard 
               into two equal-area pieces along a non-descending line from lower 
               left to upper right and passing through the center.
%H A063075 Paul D. Hanna, <a href="b063075.txt">Table of n, a(n) for n = 0..70</
               a>
%F A063075 a(n) = Sum_{k=0..n^2} A063746(n,k)^2 ; i.e. equals the sums of the squares 
               of the coefficients of q in the central q-binomial coefficients. 
               - Paul D. Hanna, Dec 12 2006
%e A063075 For a 6 X 6 board (n=3) the partition (6,6,2,2,2,0) represents a Ferrers 
               plot that does not pass through the center of a 6*6 box.
%e A063075 Central q-binomial coefficients begin:
%e A063075 1;
%e A063075 1 + q;
%e A063075 1 + q + 2*q^2 + q^3 + q^4;
%e A063075 1 + q + 2*q^2 + 3*q^3 + 3*q^4 + 3*q^5 + 3*q^6 + 2*q^7 + q^8 + q^9;
%e A063075 the coefficients of q in these polynomials form the rows of triangle 
               A063746.
%e A063075 The sums of squared terms in rows of A063746 equal this sequence.
%t A063075 Table[(#.#)&@Table[T[k, n, n], {k, 0, n^2}], {n, 0, 24}] with T[m, a, 
               b] as defined in A047993.
%Y A063075 Cf. A047993, A063074, A063746.
%Y A063075 Sequence in context: A000165 A109664 A009812 this_sequence A112541 A052667 
               A006925
%Y A063075 Adjacent sequences: A063072 A063073 A063074 this_sequence A063076 A063077 
               A063078
%K A063075 nonn
%O A063075 0,2
%A A063075 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Aug 03 2001
%E A063075 Additional comments from Paul D. Hanna (pauldhanna(AT)juno.com), Dec 
               12 2006