The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A116540

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A116540

Number of zero-one matrices with n ones and no zero rows or columns, up to permutation of rows.
(history; published version)

#29 by Alois P. Heinz at Sat Sep 23 13:46:49 EDT 2023

STATUS

proposed

approved

#28 by Andrew Howroyd at Sat Sep 23 13:45:30 EDT 2023

STATUS

editing

proposed

#27 by Andrew Howroyd at Sat Sep 23 13:45:26 EDT 2023

PROG

(PARI)

R(n, k)={Vec(-1 + 1/prod(j=1, k, (1 - x^j + O(x*x^n))^binomial(k, j) ))}

seq(n) = {concat([1], sum(k=1, n, R(n, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)) ))} \\ Andrew Howroyd, Sep 23 2023

STATUS

approved

editing

#26 by Alois P. Heinz at Fri Sep 13 20:36:46 EDT 2019

STATUS

editing

approved

#25 by Alois P. Heinz at Fri Sep 13 20:36:42 EDT 2019

LINKS

P. J. Cameron, T. Prellberg and D. Stark, <a href="http://arxiv.org/abs/math/0510155">Asymptotics for incidence matrix classes </a>, arXiv:math/0510155 [math.CO], 2005-2006.

STATUS

approved

editing

#24 by OEIS Server at Fri Sep 13 20:35:31 EDT 2019

LINKS

Alois P. Heinz, <a href="/A116540/b116540_1.txt">Table of n, a(n) for n = 0..230</a>

#23 by Alois P. Heinz at Fri Sep 13 20:35:31 EDT 2019

STATUS

editing

approved

Discussion

Fri Sep 13

20:35

OEIS Server: Installed new b-file as b116540.txt.  Old b-file is now b116540_1.txt.

#22 by Alois P. Heinz at Fri Sep 13 20:35:28 EDT 2019

LINKS

Alois P. Heinz, <a href="/A116540/b116540_1.txt">Table of n, a(n) for n = 0..200230</a>

STATUS

approved

editing

#21 by Alois P. Heinz at Fri Sep 13 20:34:51 EDT 2019

STATUS

editing

approved

#20 by Alois P. Heinz at Fri Sep 13 20:34:38 EDT 2019

MAPLE

b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0, add(b(n-i*j,

min(n-i*j, i-1), k)*binomial(binomial(k, i)+j-1, j), j=0..n/i)))

end:

a:= n-> add(add(b(n$2, i)*(-1)^(k-i)*binomial(k, i), i=0..k), k=0..n):

seq(a(n), n=0..24); # Alois P. Heinz, Sep 13 2019