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  "body": "\n## Statement\n\nLet *M*\u003csub\u003e*n*\u003c/sub\u003e denote the number of seating arrangements for *n* couples. (Touchard 1934) derived the formula\n\n$$M_n = 2 \\cdot n! \\sum_{k=0}^n (-1)^k \\frac{2n}{2n-k} {2n-k\\choose k} (n-k)!.$$\n\nMuch subsequent work has gone into alternative [[proofs|0B94TKFQJX]] for this formula and into various generalized versions of the problem.\n\nA different umbral formula for *M*\u003csub\u003e*n*\u003c/sub\u003e involving Chebyshev polynomials of first kind was given by (Wyman Moser 1958).\n",
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