This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A101370 Number of zero-one matrices with n ones and no zero rows or columns. 9
 1, 4, 24, 196, 2016, 24976, 361792, 5997872, 111969552, 2324081728, 53089540992, 1323476327488, 35752797376128, 1040367629940352, 32441861122796672, 1079239231677587264, 38151510015777089280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = (1/(4n!)) * Sum_{r, s>=0} (rs)_n / 2^(r+s) }, where (m)_n is the falling factorial m * (m-1) * ... * (m-n+1). [Maia and Mendez] REFERENCES Georg Cantor, Gesammelte Abhandlungen mathematischen und philosophischen Inhalts, p. 435 (IV, 4. Mitteilungen zur Lehre vom Transfiniten, VIII Nr. 13), Springer, Berlin. LINKS P. J. Cameron, D. A. Gewurz and F. Merola, Product action, Discrete Math., 308 (2008), 386-394. M. Maia and M. Mendez, On the arithmetic product of combinatorial species FORMULA a(n) = (Sum s(n, k) * P(k)^2)/n!, where P(n) is the number of labeled total preorders on {1, ..., n} (A000670), s are signed Stirling numbers of the first kind. G.f.: Sum_{m>=0,n>=0} Sum_{j=0..n} (-1)^(n-j)*binomial(n,j)*((1+x)^j-1)^m. - Vladeta Jovovic, Mar 25 2006 Inverse binomial transform of A007322. - Vladeta Jovovic, Aug 17 2006 G.f.: Sum_{n>=0} 1/(2-(1+x)^n)/2^(n+1). - Vladeta Jovovic, Sep 23 2006 G.f.: Sum_{n>=0} A000670(n)^2*log(1+x)^n/n! where 1/(1-x) = Sum_{n>=0} A000670(n)*log(1+x)^n/n!. [From Paul D. Hanna, Nov 07 2009] EXAMPLE a(2)=4: [1 1] [1] [1 0] [0 1] ..... [1] [0 1] [1 0] MATHEMATICA m = 17; a670[n_] = Sum[ StirlingS2[n, k]*k!, {k, 0, n}]; Rest[ CoefficientList[ Series[ Sum[ a670[n]^2*(Log[1 + x]^n/n!), {n, 0, m}], {x, 0, m}], x]] (* From Jean-François Alcover, Sep 02 2011, after g.f.  *) PROG (GAP) P:=function(n) return Sum([1..n], x->Stirling2(n, x)*Factorial(x)); end; (GAP) F:=function(n) return Sum([1..n], x->(-1)^(n-x)*Stirling1(n, x)*P(x)^2)/Factorial(n); end; (PARI) {Stirling2(n, k)=if(k<0|k>n, 0, sum(i=0, k, (-1)^i*binomial(k, i)/k!*(k-i)^n))} {A000670(n)=sum(k=0, n, Stirling2(n, k)*k!)} {a(n)=polcoeff(sum(m=0, n, A000670(m)^2*log(1+x+x*O(x^n))^m/m!), n)} /* Paul D. Hanna, Nov 07 2009 */ CROSSREFS Cf. A000670 (the sequence (P(n)). Cf. A049311 (row and column permutations allowed). Cf. A000670, A122725. [From Paul D. Hanna, Nov 07 2009] Sequence in context: A024249 A007145 A219530 * A201338 A099021 A220690 Adjacent sequences:  A101367 A101368 A101369 * A101371 A101372 A101373 KEYWORD easy,nonn,changed AUTHOR Peter J. Cameron, Jan 14 2005 EXTENSIONS Cantor reference from Rainer Rosenthal, Apr 10 2007 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .