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%I #12 Jul 31 2017 03:26:52
%S 0,1,0,3,1,0,6,3,1,0,9,5,3,1,0,12,7,4,3,1,0,15,9,6,4,3,1,0,19,12,8,6,
%T 4,3,1,0,22,14,10,8,6,4,3,1,0,26,17,12,9,7,5,4,3,1,0,30,20,15,11,9,7,
%U 5,4,3,1,0,34,23,17,14,11,9,7,5,4,3,1,0,38,26,20,16,13,10,8,7,5,4,3,1,0,42
%N Triangle of expected coupon collection numbers rounded up; i.e., if aiming to collect part of a set of n coupons, the expected number of random coupons required to receive first the set with exactly k missing.
%H Michael De Vlieger, <a href="/A071417/b071417.txt">Table of n, a(n) for n = 0..11475</a> (rows 0 <= n <= 150).
%F a(n, k) = ceiling(n*Sum_{j=k+1..n} 1/j) = ceiling(A067176(n, k)*k!/(n-1)!) = ceiling(A008279(n, n-k)*Sum_{j>=n-k} j*A008277(j-1, n-k-1)/n^j).
%e Rows start
%e 0;
%e 1,0;
%e 3,1,0;
%e 6,3,1,0;
%e 9,5,3,1,0;
%e etc.
%t Table[Ceiling[n Sum[1/j, {j, k + 1, n}]], {n, 0, 12}, {k, 0, n}] // Flatten (* _Michael De Vlieger_, Jul 30 2017 *)
%Y Cf. A060293 (left hand column), A067176.
%K nonn,tabl
%O 0,4
%A _Henry Bottomley_, May 29 2002
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