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1, 3, 8, 27, 124, 725, 5046, 40327, 362888, 3628809, 39916810, 479001611, 6227020812, 87178291213, 1307674368014, 20922789888015, 355687428096016, 6402373705728017, 121645100408832018, 2432902008176640019
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Numbers m such that n!*C(m,n) = C(m,n+1). - Lekraj Beedassy (blekraj(AT)yahoo.com), Feb 18 2006
a(n) is also the maximum size for a deck of cards in the Communicating the Card magic trick. In this game Alice draws n+1 cards from the deck at random, without replacement, and passes n of them, one by one, to her accomplice Bob. If the deck has a(n) cards or fewer, there is an algorithm by which Alice can communicate to Bob the identity of the card she chooses to retain, using only the identity and the order of passing of the n passed cards. (One side of the proof, that no larger deck size will work, is easy: the retained card can be one of (n+1)! possibilities, since Bob knows that it is not one of the n passed cards. Alice has (n+1) ways to retain a card and n! ways to order the passing of the remaining cards, so she cannot communicate more than (n+1)! different possibilities.) [From Lee A. Newberg (integer(AT)quantconsulting.com), Jun 09 2010]
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LINKS
| Author?, Communicating the Card puzzle. [From Lee A. Newberg (integer(AT)quantconsulting.com), Jun 09 2010]
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FORMULA
| a(n)=n+Sum{k*k!: k=1, 2, ..., n-1)}
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EXAMPLE
| a(5)=(5+1)!+5 = 725.
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MATHEMATICA
| Table[(n+1)!+n, {n, 0, 40}] (* From Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
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CROSSREFS
| a(n)=least k such that s(k)=n, where s=A030298.
Equals A005095(n+1) - 1.
Sequence in context: A102206 A110886 A104854 * A074271 A005641 A148845
Adjacent sequences: A030492 A030493 A030494 * A030496 A030497 A030498
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Better description from Jason Earls (zevi_35711(AT)yahoo.com), Mar 24 2001
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