|
%I #19 Aug 31 2018 16:52:26
%S 1,33,727,13365,221431,3428733,50631967,721942485,10021257511,
%T 136192514733,1819621847407,23973890545605,312209398691191,
%U 4026262617877533,51492399583946047,653858524870924725
%N Expansion of 1/((1-10x)(1-11x)(1-12x)).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (33,-362,1320)
%F If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-2) = f(n,2,10) for n >= 2. - _Milan Janjic_, Apr 26 2009
%F a(n) = 33*a(n-1) - 362*a(n-2) + 1320*a(n-3), n >= 3. - _Vincenzo Librandi_, Mar 18 2011
%F a(n) = 23*a(n-1) - 132*a(n-2) + 10^n, n >= 2. - _Vincenzo Librandi_, Mar 18 2011
%F a(n) = 6*12^(n+1) - 11^(n+2) + 5*10^(n+1). - _R. J. Mathar_, Mar 18 2011
%t CoefficientList[Series[1/((1-10x)(1-11x)(1-12x)),{x,0,30}],x] (* or *) LinearRecurrence[{33,-362,1320},{1,33,727},30] (* _Harvey P. Dale_, Apr 27 2012 *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_
|
