%I #4 Sep 20 2013 20:13:16
%S 35,66,180,660,2904,14196,73920,400620,2229624,12637956,72573360,
%T 420738780,2456635944,14422057716,85023813600,502907704140,
%U 2982460443864,17724476245476,105513644666640,628987635392700,3753738850485384,22422625749793236,134041199563164480
%N Total sum of n-th powers of parts in all partitions of 6.
%H Alois P. Heinz, <a href="/A229357/b229357.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = Sum_{k=1..6} A066633(6,k) * k^n.
%F a(n) = 19 + 8*2^n + 4*3^n + 2*4^n + 5^n + 6^n.
%F G.f.: -(18144*x^5 -28874*x^4 +17295*x^3 -4919*x^2 +669*x -35) / Product_{j=1..6} (j*x-1).
%p a:= n-> 19+8*2^n+4*3^n+2*4^n+5^n+6^n:
%p seq(a(n), n=0..30);
%Y Row n=6 of A213191.
%K nonn,easy
%O 0,1
%A _Alois P. Heinz_, Sep 20 2013
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