Problem #28
Mrs Cartman’s Desire
Mrs Cartman likes rotational symmetry (everything which is symmetric about the centre) She had a long cherished desire of playing chess. So Randy Marsh challenges her to solve the following puzzle:
She is asked to arrange the non-attacking rooks on the chessboard according to Mrs Cartman’s fantasies, only if possible. She is given chessboards of different sizes (n∗n) and asked what are the total number of ways of arranging n rooks if n varies from 1 to 61. Give the answer modulo 1000000007.