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derangement number

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1: 26.13 Permutations: Cycle Notation
See §26.8 for generating functions, recurrence relations, identities, and asymptotic approximations. … The derangement number, d ( n ) , is the number of elements of 𝔖 n with no fixed points:
26.13.4 d ( n ) = n ! j = 0 n ( 1 ) j 1 j ! = n ! + e 2 e .
2: 26.15 Permutations: Matrix Notation
The number of derangements of n is the number of permutations with forbidden positions B = { ( 1 , 1 ) , ( 2 , 2 ) , , ( n , n ) } . …
3: Bibliography Z
  • D. Zagier (1989) The Dilogarithm Function in Geometry and Number Theory. In Number Theory and Related Topics (Bombay, 1988), R. Askey and others (Eds.), Tata Inst. Fund. Res. Stud. Math., Vol. 12, pp. 231–249.
  • D. Zagier (1998) A modified Bernoulli number. Nieuw Arch. Wisk. (4) 16 (1-2), pp. 63–72.
  • J. Zeng (1992) Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials. Proc. London Math. Soc. (3) 65 (1), pp. 1–22.