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A242191 Expected value of the highest die when n six-sided dice are rolled, multiplied by 6^n. 0
21, 161, 1071, 6797, 42231, 259421, 1582791, 9614717, 58230711, 351922781, 2123580711, 12799240637, 77074749591, 463808234141, 2789504205831, 16769733474557, 100779708074871, 605475935585501, 3636808913042151, 21840480209276477, 131140458175102551, 787328413691288861 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..22.

FORMULA

a(n) = 1 + sum(k=2..6, j=1..n) k*C(n,j)*(k-1)^(n-j), where C represents binomial coefficients.

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

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.

CROSSREFS

Sequence in context: A267473 A179097 A070315 * A146301 A126993 A022681

Adjacent sequences:  A242188 A242189 A242190 * A242192 A242193 A242194

KEYWORD

nonn

AUTHOR

Andrew Woods, May 06 2014

STATUS

approved

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Last modified January 18 19:50 EST 2020. Contains 331030 sequences. (Running on oeis4.)