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A094223 Number of binary n X n matrices with all rows (columns) distinct, up to permutation of columns (rows). 13
1, 2, 7, 68, 2251, 247016, 89254228, 108168781424, 451141297789858, 6625037125817801312, 348562672319990399962384, 66545827618461283102105245248, 46543235997095840080425299916917968, 120155975713532210671953821005746669185792, 1152009540439950050422144845158703009569109376384 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Goran Kilibarda and Vladeta Jovovic, Enumeration of some classes of T_0-hypergraphs, arXiv:1411.4187 [math.CO], 2014.
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).
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 *)
PROG
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k+n-1, n)); \\ Michel Marcus, Dec 17 2022
CROSSREFS
Main diagonal of A059584 and A059587, A060690, A088309.
Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763
Sequence in context: A260968 A322223 A173226 * A217069 A323673 A366359
KEYWORD
easy,nonn
AUTHOR
Goran Kilibarda and Vladeta Jovovic, May 28 2004
EXTENSIONS
More terms from Robert G. Wilson v, May 29 2004
a(13) onwards from Andrew Howroyd, Jan 20 2024
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)