

A047929


a(n) = 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
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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). This sequence 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. For example, no 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.  Asher Auel, Jan 26 2000


LINKS



FORMULA

a(n) = 5*a(n1)  10*a(n2) + 10*a(n3)  5*a(n4) + a(n5).  Wesley Ivan Hurt, May 22 2021
Sum_{n>=3} 1/a(n) = (Pi^2  9)/12.
Sum_{n>=3} (1)^(n+1)/a(n) = Pi^2/24 + 2*log(2)  7/4. (End)


MATHEMATICA

Drop[CoefficientList[Series[6 x^3*(3 + x)/(1  x)^5, {x, 0, 34}], x], 2] (* Michael De Vlieger, May 21 2021 *)


PROG



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



