A060613 Number of n X n {-1,0,1} matrices with no zero rows.

2, 64, 17576, 40960000, 829997587232, 148863517207035904, 238534446168822298080896, 3429499272008000182681600000000, 443223773846454955204927262062339154432

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..45

Formula

a(n) = (3^n - 1)^n.

E.g.f.: Sum_{n>=0} 3^(n^2) * exp(-3^n*x) * x^n/n!. - Paul D. Hanna, Dec 26 2011

O.g.f.: Sum_{n>=0} 3^(n^2) * x^n/(1+3^n*x)^(n+1). - Paul D. Hanna, Dec 26 2011

Prog

(PARI) a(n)={(3^n - 1)^n} \\ Harry J. Smith, Jul 08 2009
(PARI) {a(n, q=3, m=1, b=-1)=(m*q^n + b)^n} \\ Paul D. Hanna, Dec 26 2011
(PARI) /* E.g.f. series identity: */
{a(n, q=3, m=1, b=-1)=n!*polcoeff(sum(k=0, n, m^k*q^(k^2)*exp(b*q^k*x+x*O(x^n))*x^k/k!), n)} \\ Paul D. Hanna, Dec 26 2011
(PARI) /* O.g.f. series identity: */
{a(n, q=3, m=1, b=-1)=polcoeff(sum(k=0, n, m^k*q^(k^2)*x^k/(1-b*q^k*x+x*O(x^n))^(k+1)), n)} \\ Paul D. Hanna, Dec 26 2011

Crossrefs

Cf. A055601, A202989.

Sequence in context: A263185 A155957 A085535 * A139772 A348214 A092238

Adjacent sequences: A060610 A060611 A060612 * A060614 A060615 A060616

Keyword

nonn

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 25 2001

Extensions

More terms from Harry J. Smith, Jul 08 2009

Status

approved