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

1,3

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

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

Prog

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

Crossrefs

Cf. A055601, A086193, A092477, A362013.

Sequence in context: A272630 A060629 A287228 * A323314 A295022 A017427

Adjacent sequences: A086203 A086204 A086205 * A086207 A086208 A086209

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 27 2003

Extensions

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

Status

approved