|
Search: id:A144223
|
|
|
| A144223 |
|
Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes. |
|
+0
2
|
|
| 1, 6, 42, 330, 2850, 26682, 268098, 2869242, 32510850, 388109562, 4861622850, 63682081530, 869725707522, 12352785293562, 182049635623362, 2778394592545530, 43833623157604482, 713738052924821754
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n) is also the exp transform of A010722. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
|
|
LINKS
|
N. J. A. Sloane, Transforms [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
|
|
FORMULA
|
a(n)=Sum_{k=0..n}6^k*A048993(n,k); A048993: Stirling-2 numbers. G.f.: 6*(x/(1-x))*A(x/(1-x))=A(x)-1; six times the binomial transform equals this sequence shifted one place left. E.g.f.:exp(6(e^x-1)).
|
|
MAPLE
|
a:= proc(n) option remember; `if` (n=0, 1, (1+add (binomial (n-1, k-1) *a(n-k), k=1..n-1)) *6) end: seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
|
|
PROGRAM
|
(Other) sage: expnums(18, 6)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
|
|
CROSSREFS
|
Cf. A000110, A001861, A027710, A078944, A144180
Sequence in context: A118351 A033296 A082302 this_sequence A029588 A001725 A123510
Adjacent sequences: A144220 A144221 A144222 this_sequence A144224 A144225 A144226
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 14 2008
|
|
EXTENSIONS
|
More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008
|
|
|
Search completed in 0.002 seconds
|
