This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016109 #31 Feb 13 2025 07:53:52
%S A016109 1,34,725,12410,186501,2571114,33339685,413066170,4941549701,
%T A016109 57504755594,654463491045,7314256515930,80522026412101,
%U A016109 875355238834474,9415203971344805,100355146006589690
%N A016109 Expansion of 1/((1-7*x)*(1-8*x)*(1-9*x)*(1-10*x)).
%H A016109 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (34,-431,2414,-5040).
%F A016109 If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,7), n >= 3. - _Milan Janjic_, Apr 26 2009; adapted by _R. J. Mathar_, Mar 15 2011
%F A016109 a(n) = 19*a(n-1) - 90*a(n-2) + 8^(n+1) - 7^(n+1), n >= 2. - _Vincenzo Librandi_, Mar 12 2011
%F A016109 a(n) = (10^(n+3) - 3*9^(n+3) + 3*8^(n+3) - 7^(n+3))/6. - _Bruno Berselli_, Mar 12 2011
%F A016109 a(n) = 34*a(n-1) - 431*a(n-2) + 2414*a(n-3) - 5040*a(n-4); a(0)=1, a(1)=34, a(2)=725, a(3)=12410. - _Harvey P. Dale_, Jan 26 2012
%t A016109 CoefficientList[Series[1/((1-7x)(1-8x)(1-9x)(1-10x)),{x,0,20}],x] (* or *) LinearRecurrence[{34,-431,2414,-5040},{1,34,725,12410},21] (* _Harvey P. Dale_, Jan 26 2012 *)
%Y A016109 Cf. A000453, A025211, A028025, A003468, A028165, A028200, A016075, A016094.
%K A016109 nonn
%O A016109 0,2
%A A016109 _Robert G. Wilson v_
%E A016109 Offset changed to 0 by _Vincenzo Librandi_, Mar 12 2011