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%I #21 Jul 08 2024 21:42:50
%S 1,24,385,5160,62401,706104,7628545,79669320,810888001,8089258584,
%T 79415935105,769621605480,7379461252801,70134974713464,
%U 661651583000065,6203106293141640,57847125937972801,537010118353326744
%N Expansion of 1/((1-7x)(1-8x)(1-9x)).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,-191,504).
%F If we define f(m,j,x)=sum(binomial(m,k)*stirling2(k,j)*x^(m-k),k=j..m) then a(n-2)=f(n,2,7), (n>=2). - _Milan Janjic_, Apr 26 2009
%F a(n) = 24*a(n-1) - 191*a(n-2) + 504*a(n-3), n>=3. - _Vincenzo Librandi_, Mar 15 2011
%F a(n) = 17*a(n-1) - 72*a(n-2) + 7^n, n>=2. - _Vincenzo Librandi_, Mar 15 2011
%F a(n) = 7^(n+2)/2 -8^(n+2) +9^(n+2)/2. - _R. J. Mathar_, Mar 15 2011
%t CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)),{x,0,20}],x] (* or *) LinearRecurrence[{24,-191,504},{1,24,385},20] (* _Harvey P. Dale_, Aug 20 2013 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_