cp's OEIS Frontend

A166322 The number of times a point sum n is attained in all 7^6 permutations of throwing 7 dice.

%I A166322 #7 Jan 30 2016 16:36:10
%S A166322 1,7,28,84,210,462,917,1667,2807,4417,6538,9142,12117,15267,18327,
%T A166322 20993,22967,24017,24017,22967,20993,18327,15267,12117,9142,6538,4417,
%U A166322 2807,1667,917,462,210,84,28,7,1
%N A166322 The number of times a point sum n is attained in all 7^6 permutations of throwing 7 dice.
%C A166322 The sum for any number of dice can be obtained by summing the trailing six terms of the sequence above - assuming leading zeros.
%C A166322 1 1 1 1 1 1
%C A166322 1 2 3 4 5 6 5 4 3 2 1
%C A166322 1 3 6 10 15 21 25 27 27 25 21 15 10 6 3 1
%C A166322 1 4 10 20 35 56 80 104 125 140 125 104 80 56 35 20 10 4 1
%C A166322 etc.
%H A166322 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dice">Dice</a>
%F A166322 F_{s,i}(k)= sum(n=0, floor((k-i)/s), (-1)^n*binomial(n,i)*binomial(i-1,k-s*n-1)).
%o A166322 (PARI) Vec(((sum(k=1,6,x^k))^7+O(x^66))) \\ _Joerg Arndt_, Mar 04 2013
%Y A166322 A056150 gives sums for 3 dice.
%Y A166322 A108907 gives sums for 6 dice.
%Y A166322 A063260 gives the sums for 2 dice through to 6 dice.
%K A166322 nonn,fini,full
%O A166322 7,2
%A A166322 Robert Goodhand (robert(AT)rgoodhand.fsnet.co.uk), Oct 11 2009