A094223 Number of binary n X n matrices with all rows (columns) distinct, up to permutation of columns (rows).
1, 2, 7, 68, 2251, 247016, 89254228, 108168781424, 451141297789858, 6625037125817801312, 348562672319990399962384, 66545827618461283102105245248, 46543235997095840080425299916917968, 120155975713532210671953821005746669185792, 1152009540439950050422144845158703009569109376384
Offset: 0
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..50
- Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
Crossrefs
Programs
-
Mathematica
a[n_] := Sum[(-1)^(n - k)*StirlingS1[n, k]*Binomial[2^k, n], {k, 0, n}]; (* or *) a[n_] := Sum[ StirlingS1[n, k]*Binomial[2^k + n - 1, n], {k, 0, n}]; Table[ a[n], {n, 0, 12}] (* Robert G. Wilson v, May 29 2004 *) -
PARI
a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k+n-1, n)); \\ Michel Marcus, Dec 17 2022
Formula
a(n) = Sum_{k=0..n} (-1)^(n-k)*Stirling1(n, k)*binomial(2^k, n).
a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k+n-1, n).
Extensions
More terms from Robert G. Wilson v, May 29 2004
a(13) onwards from Andrew Howroyd, Jan 20 2024