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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
OFFSET
1,2
LINKS
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);
MATHEMATICA
With[{nn=30}, CoefficientList[Series[1/(2-Exp[x])-1/(2-Exp[x]+x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 29 2024 *)
CROSSREFS
Column k=1 of A245733.
Sequence in context: A128103 A359489 A329789 * A078839 A243771 A026306
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 04 2014
STATUS
approved