OFFSET
0,2
COMMENTS
a(n) is the number of n X n (0,1) matrices with distinct rows modulo rows permutations. - Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 13 2003
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..60
FORMULA
G.f.: A(x) = Sum_{n>=0} log(1 + 2^n*x)^n / n!. - Paul D. Hanna, Dec 28 2007
a(n) = (1/n!) * Sum_{k=0..n} Stirling1(n, k) * 2^(n*k). - Paul D. Hanna, Feb 05 2023
From Vaclav Kotesovec, Jul 02 2016: (Start)
a(n) ~ 2^(n^2) / n!.
a(n) ~ 2^(n^2 - 1/2) * exp(n) / (sqrt(Pi) * n^(n+1/2)).
(End)
MAPLE
MATHEMATICA
Table[Binomial[2^n, n], {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2011 *)
PROG
(PARI) a(n)=binomial(2^n, n)
(PARI) /* G.f. A(x) as Sum of Series: */
a(n)=polcoeff(sum(k=0, n, log(1+2^k*x +x*O(x^n))^k/k!), n) \\ Paul D. Hanna, Dec 28 2007
(PARI) {a(n) = (1/n!) * sum(k=0, n, stirling(n, k, 1) * 2^(n*k) )}
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Feb 05 2023
(Magma) [Binomial(2^n, n): n in [0..25]]; // Vincenzo Librandi, Sep 13 2016
(Sage) [binomial(2^n, n) for n in (0..20)] # G. C. Greubel, Mar 14 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved