A084877 Number of (k,m,n)-antichains of multisets with k=3 and m=5.

0, 0, 0, 114, 649850, 678772108, 377819587984, 153135104560046, 51758494975477206, 15644366957608679376, 4400899140179858419388, 1180668574169021790713938, 306827161657039584492179842

Offset: 0

Author

Goran Kilibarda, Vladeta Jovovic, Jun 10 2003

Keywords

• nonn

Comments

By a (k,m,n)-antichain of multisets we mean an m-antichain of k-bounded multisets on an n-set. A multiset is called k-bounded if every its element has the multiplicity not greater than k-1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..415
• Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.

Crossrefs

Cf. A016269, A047707, A051112-A051118, A084869-A084883.

Programs

Mathematica

Table[(1/5!)*(243^n - 20*162^n + 60*126^n + 20*108^n + 10*98^n - 120*93^n - 120*84^n + 10*81^n + 30*78^n + 120*77^n + 120*70^n - 120*63^n + 20*56^n - 120*54^n + 240*42^n + 40*36^n - 240*31^n + 35*27^n + 60*26^n - 210*18^n + 210*14^n + 50*9^n - 100*6^n + 24*3^n), {n, 0, 1000}] (* G. C. Greubel, Oct 08 2017 *)

Formula

a(n) = (1/5!)*(243^n - 20*162^n + 60*126^n + 20*108^n + 10*98^n - 120*93^n - 120*84^n + 10*81^n + 30*78^n + 120*77^n + 120*70^n - 120*63^n + 20*56^n - 120*54^n + 240*42^n + 40*36^n - 240*31^n + 35*27^n + 60*26^n - 210*18^n + 210*14^n + 50*9^n - 100*6^n + 24*3^n).