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Search: id:A144263
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| A144263 |
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Number of ways of placing n labeled balls into n unlabeled (but7-colored) boxes . |
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+0
1
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| 1, 7, 56, 497, 4809, 50134, 558215, 6593839, 82187658, 1076193867, 14749823893, 210926792244, 3138696242941, 48485723853763, 775929767223352, 12840232627455485, 219355194338036309, 3862794707291567670
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is also the exp transform of A010727. [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
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LINKS
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N. J. A. Sloane, Transforms [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
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FORMULA
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a(n) = Sum_{k=0..n}7^k*A048993(n,k); A048993: Stirling-2 numbers . E.g.f.: Exp(7(e^x-1)). G.f.: 7*(x/(1-x))*A(x/(1-x))= A(x)-1 ; seven times the binomial transform equals this sequence shiftd one place left .
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MAPLE
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a:= proc(n) option remember; `if` (n=0, 1, (1+add (binomial (n-1, k-1) *a(n-k), k=1..n-1)) *7) end: seq (a(n), n=0..25); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008]
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PROGRAM
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(Other) sage: expnums(18, 7)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 15 2009]
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CROSSREFS
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Cf. A000110, A001861, A027710, A078944, A144180, A144223
Sequence in context: A145302 A165322 A082305 this_sequence A001730 A087751 A099345
Adjacent sequences: A144260 A144261 A144262 this_sequence A144264 A144265 A144266
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 16 2008
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EXTENSIONS
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More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 09 2008
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