

A242191


Expected value of the highest die when n sixsided 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
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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)*(k1)^(nj), where C represents binomial coefficients.
Conjecture: a(n) = 5^n3^n+6^(n+1)2^n14^n with generating function x*(21 +280*x 1365*x^2 +2954*x^3 2688*x^4 +720*x^5) / ( (x1) *(6*x1) *(4*x1) *(3*x1) *(2*x1) *(5*x1) )  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



