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%I #4 Sep 20 2013 20:46:28
%S 54,105,311,1281,6407,35745,212951,1323441,8464487,55247745,365983991,
%T 2451448401,16559916167,112602093345,769628452631,5282089330161,
%U 36372360161447,251135368228545,1737811434946871,12047233511096721,83642479068080327,581449745964789345
%N Total sum of n-th powers of parts in all partitions of 7.
%H Alois P. Heinz, <a href="/A229358/b229358.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = Sum_{k=1..7} A066633(7,k) * k^n.
%F a(n) = 30 + 11*2^n + 6*3^n + 3*4^n + 2*5^n + 6^n + 7^n.
%F G.f.: -(196356*x^6 -339112*x^5 +230407*x^4 -79457*x^3 +14759*x^2 -1407*x +54) / Product_{j=1..7} (j*x-1).
%p a:= n-> 30+11*2^n+6*3^n+3*4^n+2*5^n+6^n+7^n:
%p seq(a(n), n=0..30);
%Y Row n=7 of A213191.
%K nonn,easy
%O 0,1
%A _Alois P. Heinz_, Sep 20 2013
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