OFFSET
1,1
LINKS
Robert Israel, Table of n, a(n) for n = 1..1282
FORMULA
a(n) = 1 + Sum_{k=2..6, j=1..n} k*binomial(n,j)*(k-1)^(n-j).
Conjecture: a(n) = -5^n-3^n+6^(n+1)-2^n-1-4^n with generating function -x*(-21 +280*x -1365*x^2 +2954*x^3 -2688*x^4 +720*x^5) / ( (x-1) *(6*x-1) *(4*x-1) *(3*x-1) *(2*x-1) *(5*x-1) ) - R. J. Mathar, May 23 2014
Conjecture is true, because the probability that the highest is k is (k/6)^n - ((k-1)/6)^n for k = 1..6. - Robert Israel, Mar 09 2020
EXAMPLE
a(1) = 21, because when a die is rolled, the possible outcomes are 1,2,3,4,5,6, whose average is 21/6.
a(2) = 161 because when two dice are rolled, the expected value of the higher die is 161/36.
MAPLE
f:= n -> 6^(n+1)-add(i^n, i=1..5):
map(f, [$1..50]); # Robert Israel, Mar 09 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Woods, May 06 2014
STATUS
approved