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A239914
Total number of preferential arrangements of 1, 2, ..., n things.
3
1, 4, 17, 92, 633, 5316, 52609, 598444, 7685705, 109933268, 1732565841, 29824133436, 556682481817, 11198025452260, 241481216430113, 5557135898411468, 135927902927547369, 3521462566184392692, 96323049885512803825, 2774010846129897006940, 83898835844633970888761
OFFSET
1,2
COMMENTS
Although A217389 = a(n)+1 already exists, it is this sequence that one really needs.
LINKS
FORMULA
a(n) = Sum_{k=1..n} A000670(k).
a(n) = A217389(n) - 1.
MAPLE
b:= proc(n, k) option remember;
`if`(n=0, k!, k*b(n-1, k)+b(n-1, k+1))
end:
a:= proc(n) option remember; `if`(n=0, 0, a(n-1)+b(n, 0)) end:
seq(a(n), n=1..23); # Alois P. Heinz, Feb 20 2025
CROSSREFS
Sequence in context: A316084 A112354 A020011 * A323664 A067084 A123750
KEYWORD
nonn,changed
AUTHOR
N. J. A. Sloane, Apr 12 2014
STATUS
approved