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A245855
Number of preferential arrangements of n labeled elements such that the minimal number of elements per rank equals 2.
2
1, 0, 6, 20, 120, 672, 5516, 40140, 368640, 3521870, 37445298, 422339502, 5215454426, 68144100780, 954428684280, 14160968076584, 222769496190060, 3692874342747114, 64493471050666430, 1181830474135532130, 22692074431844298558, 455404848204906308984
OFFSET
2,3
LINKS
FORMULA
E.g.f.: 1/(2-exp(x)+x) -1/(2-exp(x)+x+x^2/2).
a(n) = A032032(n) - A102233(n) = A245732(n,2) - A245732(n,3).
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, 2) -b(n, 3):
seq(a(n), n=2..25);
CROSSREFS
Column k=2 of A245733.
Sequence in context: A267855 A099840 A223045 * A074012 A074013 A333896
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 04 2014
STATUS
approved