|
%I #22 Dec 17 2022 12:49:03
%S 1,1,3,29,1015,126651,53354350,74698954306,350688201987402,
%T 5624061753186933530,314512139441575825493524,
%U 62498777166571927258267336860,44831219113504221199415663547412096
%N 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.
%C Main diagonal of A059202.
%D G. Kilibarda and V. Jovovic, "Enumeration of some classes of T_0-hypergraphs", in
%H G. C. Greubel, <a href="/A094000/b094000.txt">Table of n, a(n) for n = 0..59</a>
%H Goran Kilibarda and Vladeta Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.
%F a(n) = Sum_{k=0..n+1} Stirling1(n+1, k)*binomial(2^(k-1)-1, n).
%F a(n) ~ binomial(2^n,n). - _Vaclav Kotesovec_, Mar 18 2014
%t 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 *)
%o (PARI) a(n) = sum(k=0, n+1, stirling(n+1, k, 1)*binomial(2^(k-1)-1, n)); \\ _Michel Marcus_, Dec 17 2022
%Y Cf. A048291, A059202, A088309.
%Y Binary matrices with distinct rows and columns, various versions: A059202, A088309, A088310, A088616, A089673, A089674, A093466, A094000, A094223, A116532, A116539, A181230, A259763
%K nonn,easy
%O 0,3
%A Goran Kilibarda and _Vladeta Jovovic_, May 30 2004
%E More terms from _Robert G. Wilson v_, Jun 01 2004
|
