0,3

a(n) enumerates (ordered) lists of n two-tuples such that all numbers from 1 to n appear as the first as well as the second tuple entry, and the j-th list member is not the tuple (j,j), for every j=1,..,n. Called coincidence-free 2-tuple lists of length n. See the Charalambides reference for this combinatorial interpretation. - Charalambides reference and comments with combinatorial examples from W. Lang, Jan 21 2008.

Ch. A. Charalambides, Enumerative Combinatorics, Chapman & Hall/CRC, Boca Raton, Florida, 2002, p. 187, Exercise 13.(a), for r=2.

G.f.: hypergeom([1, 1, 1], [], x/(1+x))/(1+x).

E.g.f.: exp(-x)* hypergeom([1, 1], [], x).

a(n) = n^2*a(n-1)+n*(n-1)*a(n-2)+(-1)^n. - Vladeta Jovovic (vladeta(AT)Eunet.yu), Jul 15 2004

a(n)=sum(((-1)^(n-j))*binomial(n,j)*(j!)^2,j=0..n). See the Charalambides reference a(n)=B_{n,2}. - Charalambides reference and comments with combinatorial examples from W. Lang, Jan 21 2008.

2-tupel combinatorics: a(1)=0 because the only list of 2-tupels with numbers 1 is [(1,1)], and this is a coincidence for j=1.

2-tupel combinatorics: the a(2)=3 coincidence free 2-tupel lists of length n=2 are [(1,2),(2,1)], [(2,1),(1,2)] and [(2,2),(1,1)]. The list [(1,1),(2,2)] has two coincidences (j=1 and j=2).

Cf. A001044, A046662(binomial transform of squares of factorial numbers).

(-1)^n times the polynomials in A099599 evaluated at -1.

Sequence in context: A136046 A122949 A049088 this_sequence A059511 A112676 A103112

Adjacent sequences: A089038 A089039 A089040 this_sequence A089042 A089043 A089044

easy,nonn

Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 03 2003

Charalambides reference and comments with combinatorial examples from W. Lang, Jan 21 2008.