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A094000
Number of n X n (0,1)-matrices with no zero rows or columns and with all rows distinct and all columns distinct, up to permutation of rows.
16
1, 1, 3, 29, 1015, 126651, 53354350, 74698954306, 350688201987402, 5624061753186933530, 314512139441575825493524, 62498777166571927258267336860, 44831219113504221199415663547412096
OFFSET
0,3
COMMENTS
Main diagonal of A059202.
REFERENCES
G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in
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} Stirling1(n+1, k)*binomial(2^(k-1)-1, n).
a(n) ~ binomial(2^n,n). - Vaclav Kotesovec, Mar 18 2014
MATHEMATICA
f[n_] := Sum[ StirlingS1[n + 1, k] Binomial[2^(k - 1) - 1, n], {k, 0, n + 1}]; Table[ f[n], {n, 0, 12}] (* Robert G. Wilson v, Jun 01 2004 *)
PROG
(PARI) a(n) = sum(k=0, n+1, stirling(n+1, k, 1)*binomial(2^(k-1)-1, n)); \\ Michel Marcus, Dec 17 2022
CROSSREFS
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: A065072 A088389 A270883 * A162085 A182385 A255597
KEYWORD
nonn,easy
AUTHOR
Goran Kilibarda and Vladeta Jovovic, May 30 2004
EXTENSIONS
More terms from Robert G. Wilson v, Jun 01 2004
STATUS
approved