%I #20 May 21 2017 15:23:14
%S 3,-9,6,36,150,540,1806,5796,18150,55980,171006,519156,1569750,
%T 4733820,14250606,42850116,128746950,386634060,1160688606,3483638676,
%U 10454061750,31368476700,94118013006,282379204836,847187946150,2541664501740,7625194831806
%N A(k,3) where A(k,n) = Sum_{m=1..k} (-1)^(m+1) *binomial(n,m)*m^k.
%H Colin Barker, <a href="/A179483/b179483.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F a(n) = A001117(n), n>=3. - _R. J. Mathar_, Jul 20 2010
%F From _Colin Barker_, May 21 2017: (Start)
%F G.f.: 3*x*(1 - 9*x + 31*x^2 - 39*x^3 + 18*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F a(n) = 3 - 3*2^n + 3^n for n>2.
%F a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>5.
%F (End)
%p A179483 := proc(n) add( (-1)^(m+1)*binomial(3,m)*m^n,m=1..n) ; end proc: # _R. J. Mathar_, Jan 31 2011
%t Sum[(-1)^(m+1)Binomial[3,m]m^k,{m,1,k}]
%o (PARI) Vec(3*x*(1 - 9*x + 31*x^2 - 39*x^3 + 18*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)) + O(x^30)) \\ _Colin Barker_, May 21 2017
%Y Cf. A001117.
%K sign,easy
%O 1,1
%A _M. Lawrence Glasser_, Jul 16 2010