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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)