Search: id:A060293
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%I A060293
%S A060293 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,
%T A060293 96,101,106,110,115,120,125,130,135,141,146,151,156,161,166,172,177,
%U A060293 182,188,193,198,204,209,215,220,225,231,236,242,248,253,259,264,270
%N A060293 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.
%D A060293 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]
%F A060293 a(n) =ceiling[n*sum_{1->n}(1/k)] =ceiling[n*A001008(n)/A002805(n)] =A052488(n)+1 
               for n>2
%e A060293 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.
%p A060293 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]
%Y A060293 Sequence in context: A070021 A083354 A156242 this_sequence A123581 A084515 
               A084525
%Y A060293 Adjacent sequences: A060290 A060291 A060292 this_sequence A060294 A060295 
               A060296
%K A060293 easy,nonn
%O A060293 0,3
%A A060293 Henry Bottomley (se16(AT)btinternet.com), Mar 24 2001

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