This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A215582 The number of proper mergings of two n-antichains. 1
 1, 3, 35, 1275, 154115, 71994363, 140595475715, 1133624776334235, 36970581556591250435, 4838797912961323412254203, 2535793883977350841761956006915, 5317221866238397002010248863448839835, 44602260230569982664472646479956459441496835, 1496585236610867406252010206465708857876795888774523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The number of proper mergings of an n-antichain and an m-antichain can be computed with the following formula: a(m,n)=Sum_{i+j+k=m} m!/(i!j!k!)*(-1)^k*(2^i+2^j-1)^n. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..50 H. Mühle, Counting Proper Mergings of Chains and Antichains, arXiv:1206.3922. FORMULA a(n)=Sum_{i+j+k=n}{n!/(i!j!k!)*(-1)^k*(2^i+2^j-1)^n}. limit n->infinity a(n)/(2^(n^2))=2 [From Vaclav Kotesovec, Aug 23 2012] EXAMPLE For n=1, the a(1)=3 proper mergings of two 1-antichains ({a},{}) and ({b},{}) are the following three posets: ({a,b},{}), ({a,b},{(a,b)}), ({a,b},{(b,a)}). MATHEMATICA Table[Sum[Sum[Sum[If[i+j+k==n, n!/(i!j!k!)*(-1)^k*(2^i+2^j-1)^n, 0], {i, 0, n}], {j, 0, n}], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 23 2012 *) CROSSREFS Sequence in context: A062699 A012767 A279377 * A136525 A136556 A006098 Adjacent sequences:  A215579 A215580 A215581 * A215583 A215584 A215585 KEYWORD easy,nonn AUTHOR Henri Mühle, Aug 21 2012 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 April 21 06:42 EDT 2019. Contains 322310 sequences. (Running on oeis4.)