The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A104602 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A104602

Number of square (0,1)-matrices with exactly n entries equal to 1 and no zero row or columns.
(history; published version)

#17 by Vaclav Kotesovec at Sun May 03 05:15:41 EDT 2015

FORMULA

In closed form, c = 1 / (log(2) * 2^(log(2)/2+2) * sqrt(Pi*(1-log(2)))). - Vaclav Kotesovec, May 03 2015

STATUS

approved

editing

#16 by Alois P. Heinz at Wed Jan 14 19:54:35 EST 2015

STATUS

editing

approved

#15 by Alois P. Heinz at Wed Jan 14 19:54:30 EST 2015

LINKS

Alois P. Heinz, <a href="/A104602/b104602.txt">Table of n, a(n) for n = 0..400</a>

#14 by Alois P. Heinz at Wed Jan 14 19:54:02 EST 2015

DATA

1, 1, 2, 10, 70, 642, 7246, 97052, 1503700, 26448872, 520556146, 11333475922, 270422904986, 7016943483450, 196717253145470, 5925211960335162, 190825629733950454, 6543503207678564364, 238019066600097607402, 9153956822981328930170, 371126108428565106918404

#13 by Alois P. Heinz at Wed Jan 14 19:39:19 EST 2015

DATA

OFFSET

1,2

0,3

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jan 14 2015

STATUS

approved

editing

#12 by Vaclav Kotesovec at Wed May 07 11:55:44 EDT 2014

STATUS

editing

approved

#11 by Vaclav Kotesovec at Wed May 07 11:55:37 EDT 2014

FORMULA

a(n) ~ c * n! / (sqrt(n) * (log(2))^(2*n)), where c = 0.28889864564457451375789435201798... . - Vaclav Kotesovec, May 07 2014

#10 by Vaclav Kotesovec at Wed May 07 11:46:14 EDT 2014

MATHEMATICA

Table[1/n!*Sum[StirlingS1[n, k]*Sum[(m!)^2*StirlingS2[k, m]^2, {m, 0, k}], {k, 0, n}], {n, 1, 20}] (* Vaclav Kotesovec, May 07 2014 *)

STATUS

approved

editing

#9 by R. J. Mathar at Fri Nov 15 14:56:14 EST 2013

STATUS

editing

approved

#8 by R. J. Mathar at Fri Nov 15 14:56:04 EST 2013

REFERENCES

H. Cheballah, S. Giraudo, R. Maurice, Combinatorial Hopf algebra structure on packed square matrices, arXiv preprint arXiv:1306.6605, 2013

LINKS

H. Cheballah, S. Giraudo, R. Maurice, <a href="http://arxiv.org/abs/1306.6605">Combinatorial Hopf algebra structure on packed square matrices</a>, arXiv preprint arXiv:1306.6605, 2013

AUTHOR

_Ralf Stephan, _, Mar 27 2005

STATUS

approved

editing