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A071417 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. 1
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150).

FORMULA

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).

EXAMPLE

Rows start

0;

1,0;

3,1,0;

6,3,1,0;

9,5,3,1,0;

etc.

MATHEMATICA

Table[Ceiling[n Sum[1/j, {j, k + 1, n}]], {n, 0, 12}, {k, 0, n}] // Flatten (* Michael De Vlieger, Jul 30 2017 *)

CROSSREFS

Cf. A060293 (left hand column), A067176.

Sequence in context: A135670 A096754 A021767 * A096653 A308639 A213668

Adjacent sequences:  A071414 A071415 A071416 * A071418 A071419 A071420

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, May 29 2002

STATUS

approved

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)