

A047929


n^2*(n1)*(n2).


5



0, 18, 96, 300, 720, 1470, 2688, 4536, 7200, 10890, 15840, 22308, 30576, 40950, 53760, 69360, 88128, 110466, 136800, 167580, 203280, 244398, 291456, 345000, 405600, 473850, 550368, 635796, 730800, 836070, 952320, 1080288, 1220736
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

2,2


COMMENTS

There are 5 ways to put parentheses in the expression a  b  c  d: (a  (b  c))  d, ((a  b)  c)  d, (a  b)  (c  d), a  (b  (c  d)), a  ((b  c)  d). A047929 describes how many sets of natural numbers [a,b,c,d] can be produced with the numbers {0,1,2,3,...n} such that all the distinct expressions take different values. A045991 describes the similar process for a  b  c.  Asher Natan Auel (auela(AT)reed.edu), Jan 26 2000
For n>=3, a(n)/6 is the number of permutations of n symbols that 3commute with an ncycle (see A233440 for definition).  Luis Manuel Rivera MartÃnez, Feb 24 2014


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Luis Manuel Rivera, Integer sequences and kcommuting permutations, arXiv preprint arXiv:1406.3081, 2014
Index entries for sequences related to parenthesizing
Index entries for linear recurrences with constant coefficients, signature (5,10,10,5,1).


FORMULA

a(n) = A004320(n2)*6.


EXAMPLE

For example, no such sets can be produced with only 0's or only 0's and 1's; with {0,1,2,3}, 18 such sets can be produced.


PROG

(MAGMA) [n^2*(n1)*(n2): n in [2..40]]; // Vincenzo Librandi, May 02 2011
(PARI) a(n)=n^4  3*n^3 + 2*n^2 \\ Charles R Greathouse IV, May 02, 2011


CROSSREFS

Cf. A045991.
Sequence in context: A186122 A275253 A034725 * A243995 A264202 A324304
Adjacent sequences: A047926 A047927 A047928 * A047930 A047931 A047932


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



