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A245854 Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 1. 2
1, 2, 12, 68, 520, 4542, 46550, 540136, 7045020, 101865410, 1619046418, 28053492348, 526430246264, 10636085523910, 230214619661790, 5314695463338704, 130356558777712468, 3385311352838750538, 92797887464933030762, 2677623216872061223780, 81123642038690958720048 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

FORMULA

E.g.f.: 1/(2-exp(x))-1/(2-exp(x)+x).

a(n) = A000670(n) - A032032(n) = A245732(n,1) - A245732(n,2).

MAPLE

b:= proc(n, k) option remember; `if`(n=0, 1,

      add(b(n-j, k)*binomial(n, j), j=k..n))

    end:

a:= n-> b(n, 1) -b(n, 2):

seq(a(n), n=1..25);

CROSSREFS

Column k=1 of A245733.

Cf. A000670, A032032, A245732.

Sequence in context: A245997 A128103 A329789 * A078839 A243771 A026306

Adjacent sequences:  A245851 A245852 A245853 * A245855 A245856 A245857

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 04 2014

STATUS

approved

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Last modified June 23 11:29 EDT 2021. Contains 345397 sequences. (Running on oeis4.)