OFFSET
1,3
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..420
FORMULA
a(n) ~ n! * n^2 / (8 * (log(2))^(n+1)). - Vaclav Kotesovec, May 03 2015
EXAMPLE
The 13 preferential arrangements on 3 points and the number of times the pattern 1<2 occurs are:
1<2<3, 3
1<3<2, 2
2<1<3, 2
2<3<1, 1
3<1<2, 1
3<2<1, 0
1=2<3, 2
1=3<2, 1
2=3<1, 0
1<2=3, 2
2<1=3, 1
3<1=2, 0
1=2=3, 0,
for a total of a(3) = 15.
MAPLE
b:= proc(n, t) option remember; `if`(n=0, [1, 0], add((p-> p+
[0, p[1]*j*t/2])(b(n-j, t+j))*binomial(n, j), j=1..n))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=1..25); # Alois P. Heinz, Dec 08 2014
MATHEMATICA
b[n_, t_] := b[n, t] = If[n == 0, {1, 0}, Sum[Function[{p}, p + {0, p[[1]]*j*t/2}][b[n - j, t + j]]*Binomial[n, j], {j, 1, n}]]; a[n_] := b[n, 0][[2]]; Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Jun 08 2015, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 13 2014
EXTENSIONS
a(8)-a(20) from Alois P. Heinz, Dec 08 2014
STATUS
approved