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A180291 Number of arrangements of n indistinguishable balls in n boxes with the maximum number of balls in any box equal to n-1. 3
1, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 156, 182, 210, 240, 272, 306, 342, 380, 420, 462, 506, 552, 600, 650, 702, 756, 812, 870, 930, 992, 1056, 1122, 1190, 1260, 1332, 1406, 1482, 1560, 1640, 1722, 1806, 1892, 1980, 2070, 2162, 2256, 2352, 2450, 2550 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

To clarify a slight ambiguity in the definition, the heaviest box in such an arrangement should contain exactly n-1 balls. - Gus Wiseman, Sep 22 2016

Conjecture: For n>1, a(n) = 2*A000217(n+1). - Bruce J. Nicholson, Apr 05 2017

LINKS

R. H. Hardin, Table of n, a(n) for n=2..59

FORMULA

Empirical: a(n) = n*binomial(n-1,n-2) for n>2.

Empirical: a(n) = A002378(n-1) for n>2. - R. J. Mathar, Sep 06 2010

Empirical: a(n) = n^2-n for n>2. a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>5. G.f.: x^2*(1+3*x-3*x^2+x^3)/(1-x)^3. - Colin Barker, Mar 18 2012

CROSSREFS

(n-1)-th entry in rows of A180281.

Sequence in context: A116368 A290467 A007622 * A056930 A326378 A064971

Adjacent sequences:  A180288 A180289 A180290 * A180292 A180293 A180294

KEYWORD

nonn

AUTHOR

R. H. Hardin, formula from Robert Gerbicz in the Sequence Fans Mailing List, Aug 24 2010

STATUS

approved

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Last modified November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)