A002416 - OEIS (original) (raw)

For n >= 1, a(n) is the number of n X n (0, 1) matrices.

Also number of directed graphs on n labeled nodes allowing self-loops (cf. A053763).

1/2^(n^2) is the Hankel transform of C(n, n/2)*(1 + (-1)^n)/(2*2^n), or C(2n, n)/4^n with interpolated zeros. - Paul Barry, Sep 27 2007

a(n) is also the order of the semigroup (monoid) of all binary relations on an n-set. - Abdullahi Umar, Sep 14 2008

With offset = 1, a(n) is the number of n X n (0, 1) matrices with an even number of 1's in every row and in every column. - Geoffrey Critzer, May 23 2013

a(n) is the number of functions from an n-set to its power set (by definition of function including the empty function only when n = 0). - Rick L. Shepherd, Dec 27 2014