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Search: id:A060293
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| A060293 |
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Expected coupon collection numbers rounded up; i.e. if aiming to collect a set of n coupons, the expected number of random coupons required to receive the full set. |
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+0
4
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| 0, 1, 3, 6, 9, 12, 15, 19, 22, 26, 30, 34, 38, 42, 46, 50, 55, 59, 63, 68, 72, 77, 82, 86, 91, 96, 101, 106, 110, 115, 120, 125, 130, 135, 141, 146, 151, 156, 161, 166, 172, 177, 182, 188, 193, 198, 204, 209, 215, 220, 225, 231, 236, 242, 248, 253, 259, 264, 270
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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R. Wyss, Identitaeten bei den Stirling-Zahlen 2. Art aus kombinatorischen Ueberlegungen beim Wuerfelspiel, Elem. Math. 51 (1996) 102-106, Eq (5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2009]
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FORMULA
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a(n) =ceiling[n*sum_{1->n}(1/k)] =ceiling[n*A001008(n)/A002805(n)] =A052488(n)+1 for n>2
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EXAMPLE
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a(2)=3 since the prob of getting both coupons after two is 1/2, after 3 is 1/4, after 4 is 1/8, etc. and 2/2+3/2^2+4/2^3+.... =3.
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MAPLE
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A001008 := proc(n) local i ; numer(add(1/i, i=1..n)) ; end: A002805 := proc(n) local i ; denom(add(1/i, i=1..n)) ; end: A060293 := proc(n) ceil(n*A001008(n)/A002805(n)) ; end: for n from 0 to 100 do printf("%d, ", A060293(n)) ; end: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2009]
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CROSSREFS
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Adjacent sequences: A060290 A060291 A060292 this_sequence A060294 A060295 A060296
Sequence in context: A083354 A135943 A156242 this_sequence A123581 A084515 A084525
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Mar 24 2001
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