A229360 - OEIS

%I #4 Sep 20 2013 20:59:59

%S 128,270,910,4392,26218,177120,1292410,9924912,78974938,644749920,

%T 5365004410,45294444432,386724933658,3331246259520,28899114836410,

%U 252142576067952,2210222303020378,19448976596389920,171690169932572410,1519690359242075472,13481625657159443098

%N Total sum of n-th powers of parts in all partitions of 9.

%H Alois P. Heinz, <a href="/A229360/b229360.txt">Table of n, a(n) for n = 0..500</a>

%F a(n) = Sum_{k=1..9} A066633(9,k) * k^n.

%F a(n) = 67 + 26*2^n + 15*3^n + 8*4^n + 5*5^n + 3*6^n + 2*7^n + 8^n + 9^n.

%F G.f.: -2*(16152120*x^8 -31900986*x^7 +26059495*x^6 -11585520*x^5 +3083861*x^4 -505629*x^3 +50060*x^2 -2745*x +64) / Product_{j=1..9} (j*x-1).

%p a:= n-> 67+26*2^n+15*3^n+8*4^n+5*5^n+3*6^n+2*7^n+8^n+9^n:

%p seq(a(n), n=0..30);

%Y Row n=9 of A213191.

%K nonn,easy

%O 0,1

%A _Alois P. Heinz_, Sep 20 2013