0,2

Also the number of n X n (0,1) matrices modulo rows permutation (by symmetry this is the same as the number of (0,1) matrices modulo columns permutation), i.e. the number of equivalence classes where two matrices A and B are equivalent if one of them is the result of permuting the rows of the other. The total number of (0,1) matrices is in sequence A002416.

a(n) = [x^n] 1/(1-x)^(2^n).

a(n) = (1/n!)*Sum((-1)^(n-k)*Stirling1(n, k)*2^(k*n), k=0..n). - Vladeta Jovovic (vladeta(AT)Eunet.yu), May 28 2004

a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(2^n+n,k) = Sum_{k=0..n} Stirling1(n,k)*(2^n+n-1)^k. G.f.: Sum_{n>=0} (-ln(1-2^n*x))^n/n!. - Paul Hanna and Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 21 2008

G.f.: A(x) = Sum_{n>=0} [ -log(1 - 2^n*x)]^n / n!. More generally, Sum_{n>=0} [ -log(1 - q^n*x)]^n/n! = Sum_{n>=0} C(q^n+n-1,n)*x^n ; also Sum_{n>=0} log(1 + q^n*x)^n/n! = Sum_{n>=0} C(q^n,n)*x^n. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 29 2007

with(combinat): for n from 1 to 20 do printf(`%d, `, binomial(2^n+n-1, n)) od:

(PARI) a(n)=binomial(2^n+n-1, n)

(PARI) {a(n)=polcoeff(sum(k=0, n, (-log(1-2^k*x +x*O(x^n)))^k/k!), n)} - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 29 2007

Cf. A002416, A060336, A088309, A132683, A132684.

Adjacent sequences: A060687 A060688 A060689 this_sequence A060691 A060692 A060693

Sequence in context: A006121 A110951 A120597 this_sequence A005617 A013038 A005321

nonn

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 19 2001

More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 20 2001

Edited by njas, Mar 17 2008