The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A274778 Number of proper mergings of an n-antichain and an n-chain. 0
 0, 3, 26, 442, 12899, 582381, 37700452, 3315996468, 380835212037, 55380159334315, 9950025870043126, 2165134468142294430, 561245519520167902471, 170913803045738754172185, 60421582956702701927410120, 24543570079301728283314502248, 11353373604627607560431407875081 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is also the number of monotone (n+1)-colorings of a complete bipartite digraph K(n,n), where a monotone (n+1)-coloring is a labeling w of the vertices of K(n,n) with integers in {1,2,...,n+1} such that for every arc (e1, e2) we have w(e1) <= w(e2). LINKS H. Mühle, Counting Proper Mergings of Chains and Antichains, Discrete Math., Vol. 327(C), 2014, 118-129. Also arXiv:1206.3922 [math.CO], 2012. FORMULA a(n) = Sum_{i=1..n+1} ((n+2-i)^n - (n+1-i)^n)*i^n. EXAMPLE For n=1, the three proper mergings of a 1-chain {x} and a 1-antichain {y} are x add(((n-i+1)^n-(n-i)^n)*(i+1)^n, i=0..n): seq(a(n), n=0..16); # Peter Luschny, Nov 11 2016 MATHEMATICA a[0] = 0; a[n_] := Sum[((n-i+1)^n - (n-i)^n)*(i+1)^n, {i, 0, n}]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Jul 14 2018, after Peter Luschny *) PROG (PARI) a(n) = sum(i=1, n+1, ((n+2-i)^n - (n+1-i)^n)*i^n); \\ Michel Marcus, Jul 14 2018 CROSSREFS Cf. A085465. Sequence in context: A182958 A174423 A321183 * A049088 A089041 A059511 Adjacent sequences:  A274775 A274776 A274777 * A274779 A274780 A274781 KEYWORD nonn AUTHOR Henri Mühle, Nov 11 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 22 16:01 EDT 2021. Contains 345386 sequences. (Running on oeis4.)