OFFSET
0,2
COMMENTS
Two such matrices are equivalent if they differ just by a permutation of the rows.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..59
G. Kilibarda and V. Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k, n). - Vladeta Jovovic, Nov 07 2003
a(n) = A088310(n) / n!.
EXAMPLE
a(2) = 5: 00/01, 00/10, 01/10, 01/11, 10/11.
MATHEMATICA
Table[A088309[n], {n, 0, 30}] (* G. C. Greubel, Dec 15 2022 *)
PROG
(Magma)
A088309:= func< n | (&+[Binomial(2^k, n)*StirlingFirst(n, k): k in [0..n]]) >;
[A088309(n): n in [0..30]]; // G. C. Greubel, Dec 15 2022
(SageMath)
@CachedFunction
def A088309(n): return (-1)^n*sum((-1)^k*binomial(2^k, n)*stirling_number1(n, k) for k in (0..n))
[A088309(n) for n in range(31)] # G. C. Greubel, Dec 15 2022
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k, n)); \\ Michel Marcus, Dec 16 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 07 2003
EXTENSIONS
Suggested by Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 06 2003
a(0)-a(5) from W. Edwin Clark, Nov 07 2003
STATUS
approved