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A240799 Total number of occurrences of the pattern 1=2<3 in all preferential arrangements (or ordered partitions) of n elements. 1
0, 0, 1, 20, 310, 4660, 72485, 1193080, 20938764, 392485560, 7850724915, 167242351100, 3785057708146, 90775554103052, 2301045251519105, 61499717442074800, 1729026306941190680, 51022485837639054768, 1577126907722325214959, 50967150013960792511700 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

There are A000670(n) preferential arrangements of n elements - see A000670, A240763.

The number that avoid the pattern 1=2<3 is given in A001710 (1,3,12,60,360,...).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..420

FORMULA

a(n) ~ n! * n^2 / (24 * (log(2))^n). - Vaclav Kotesovec, May 03 2015

MAPLE

b:= proc(n, t) option remember; `if`(n=0, [1, 0], add((p-> p+

      [0, p[1]*j*(j-1)*t/6])(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*(j-1)*t/6}][b[n-j, t+j]]*Binomial[n, j], {j, 1, n}]]; a[n_] := b[n, 0][[2]]; Table[a[n], {n, 1, 25}] (* Jean-Fran├žois Alcover, Feb 28 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A000670, A240763, A240796-A240800, A001710.

Sequence in context: A016188 A006300 A282372 * A281931 A034094 A011197

Adjacent sequences:  A240796 A240797 A240798 * A240800 A240801 A240802

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 13 2014

EXTENSIONS

a(8)-a(20) from Alois P. Heinz, Dec 08 2014

STATUS

approved

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Last modified November 28 01:24 EST 2021. Contains 349396 sequences. (Running on oeis4.)