|
| |
|
|
A084876
|
|
Number of (k,m,n)-antichains of multisets with k=3 and m=4.
|
|
0
| |
|
|
0, 0, 0, 310, 159300, 32389900, 4469327850, 503689260970, 50466655894200, 4701945998612200, 418104908350395750, 36055756736065208230, 3046399249526576159700, 253883533322134812268900
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
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
| Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
|
|
|
FORMULA
| 1/4!*(81^n - 12*54^n + 24*42^n + 4*36^n - 24*31^n + 6*27^n + 6*26^n - 36*18^n + 36*14^n + 11*9^n - 22*6^n + 6*3^n).
G.f. -10*x^3*(-31-5173*x +663390*x^2 -16812297*x^3 -320866029*x^4 +19383439320*x^5 -243502067160*x^6 +252158125680*x^7 +6816687418800*x^8) / ( (6*x-1) *(54*x-1) *(42*x-1) *(3*x-1) *(9*x-1) *(27*x-1) *(31*x-1) *(26*x-1) *(18*x-1) *(81*x-1) *(36*x-1) *(14*x-1) ). - R. J. Mathar, Jul 08 2011
|
|
|
CROSSREFS
| Cf. A016269, A047707, A051112-A051118, A084869-A084883.
Sequence in context: A051981 A134549 A206233 * A190567 A060339 A046016
Adjacent sequences: A084873 A084874 A084875 * A084877 A084878 A084879
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Goran Kilibarda, Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 10 2003
|
| |
|
|
