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A097900 Number of runs of length 1 in all permutations of [n]. (The permutation 3574162 has two runs of length 1: 357/4/16/2). 2
1, 2, 7, 32, 180, 1200, 9240, 80640, 786240, 8467200, 99792000, 1277337600, 17643225600, 261534873600, 4140968832000, 69742632960000, 1244905998336000, 23475370254336000, 466306218233856000, 9731608032706560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the number of corners in the set of tree-like tableaux of size n (see Gao et al. link). - Michel Marcus, Nov 18 2015

REFERENCES

Ira. M. Gessel, Generating functions and enumeration of sequences, Ph. D. Thesis, MIT, 1977.

LINKS

Table of n, a(n) for n=1..20.

Alice L.L. Gao, Emily X.L. Gao, Brian Y. Sun, Zubieta's Conjecture on the Enumeration of Corners in Tree-like Tableaux, arXiv:1511.05434 [math.CO], 2015.

FORMULA

a(n) = n!(n+4)/6 for n>=2.

E.g.f.: x*(6-6*x+x^2)/(6*(1-x)^2.

EXAMPLE

a(3)=7 because there are 7 runs of length 1 in the permutations 123, 13(2), (2)13, 23(1), (3)12, (3)(2)(1) (shown between parentheses).

MAPLE

1, seq(n!*(n+4)/6, n=2..23);

MATHEMATICA

Join[{1}, Table[n! (n + 4)/6, {n, 2, 20}]] (* Vincenzo Librandi, Nov 18 2015 *)

PROG

(MAGMA) [1] cat [Factorial(n)*(n+4)/6: n in [2..25]]; // Vincenzo Librandi, Nov 18 2015

CROSSREFS

Sequence in context: A006014 A121555 A265165 * A198891 A000153 A006154

Adjacent sequences:  A097897 A097898 A097899 * A097901 A097902 A097903

KEYWORD

nonn

AUTHOR

Emeric Deutsch and Ira M. Gessel, Sep 03 2004

STATUS

approved

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Last modified April 25 08:23 EDT 2017. Contains 285348 sequences.