STATUS
reviewed
approved
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Revision History for A088309
(Bold, blue-underlined text is an addition; faded, red-underlined text is aShowing entries 1-10 | older changes
Number of equivalence classes of n X n (0,1)-matrices with all rows distinct and all columns distinct.
(history; published version)
(history; published version)
STATUS
proposed
reviewed
STATUS
editing
proposed
PROG
(PARI) a(n) = sum(k=0, n, stirling(n, k, 1)*binomial(2^k, n)); \\ Michel Marcus, Dec 16 2022
FORMULA
a(n) = Sum_{k=0..n} Stirling1(n, k)*binomial(2^k, n). - Vladeta Jovovic, Nov 07 2003
REFERENCES
G. Kilibarda and Vladeta Jovovic, "Enumeration of some classes of T_0-hypergraphs", in preparation, 2004.
LINKS
G. Kilibarda and V. Jovovic, <a href="https://arxiv.org/abs/1411.4187">Enumeration of some classes of T_0-hypergraphs</a>, arXiv:1411.4187 [math.CO], 2014.
STATUS
proposed
editing
STATUS
editing
proposed
LINKS
G. C. Greubel, <a href="/A088309/b088309.txt">Table of n, a(n) for n = 0..59</a>
MATHEMATICA
A088309[n_]:= A088309[n]=Sum[Binomial[2^j, n]*StirlingS1[n, j], {j, 0, n}];
Table[A088309[n], {n, 0, 30}] (* G. C. Greubel, Dec 15 2022 *)
PROG
(Magma)
A088309:= func< n | (&+[Binomial(2^k, n)*StirlingFirst(n, k): k in [0..n]]) >;
[A088309(n): n in [0..30]]; // G. C. Greubel, Dec 15 2022
(SageMath)
@CachedFunction
def A088309(n): return (-1)^n*sum((-1)^k*binomial(2^k, n)*stirling_number1(n, k) for k in (0..n))
[A088309(n) for n in range(31)] # G. C. Greubel, Dec 15 2022
CROSSREFS
STATUS
approved
editing
STATUS
editing
approved