A086206 Number of n X n matrices with entries in {0,1} with no zero row and with zero main diagonal.

0, 1, 27, 2401, 759375, 887503681, 3938980639167, 67675234241018881, 4558916353692287109375, 1213972926354344043087129601, 1284197945649659948122178573052927, 5412701932445852698371002894178179850241, 91054366938067173656011584805755385081787109375

Offset: 1

Author

Vladeta Jovovic, Aug 27 2003

Keywords

• easy
• nonn

Comments

Equivalently a(n) is the number of labeled digraphs on [n] with no out-nodes. Cf. A362013. - Geoffrey Critzer, Apr 13 2023

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A055601, A086193, A092477, A362013.

Programs

PARI

a(n) = {(2^(n-1)-1)^n} \\ Andrew Howroyd, Jan 05 2020

Formula

a(n) = (2^(n-1)-1)^n = Sum_{k=0..n} (-1)^k*binomial(n, k)*2^((n-k)*(n-1)).

a(n) = A092477(n, n-1).

Sum_{n>=0} a(n)*x^n/A011266(n) = (Sum_{n>=0} (-x)^n/A011266(n))*(Sum_{n>=0} 2^(n(n-1))*x^n/A011266(n)). - Geoffrey Critzer, Apr 13 2023

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 05 2020