A060613 - OEIS

%I #20 Jul 03 2018 02:33:33

%S 2,64,17576,40960000,829997587232,148863517207035904,

%T 238534446168822298080896,3429499272008000182681600000000,

%U 443223773846454955204927262062339154432

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

%H Harry J. Smith, <a href="/A060613/b060613.txt">Table of n, a(n) for n = 1..45</a>

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

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

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

%o (PARI) a(n)={(3^n - 1)^n} \\ _Harry J. Smith_, Jul 08 2009

%o (PARI) {a(n, q=3, m=1, b=-1)=(m*q^n + b)^n} \\ _Paul D. Hanna_, Dec 26 2011

%o (PARI) /* E.g.f. series identity: */

%o {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

%o (PARI) /* O.g.f. series identity: */

%o {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

%Y Cf. A055601, A202989.

%K nonn

%O 1,1

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

%E More terms from _Harry J. Smith_, Jul 08 2009