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 A016307 #40 May 04 2025 15:15:51
%S A016307 1,18,232,2640,28336,295008,3020032,30620160,308720896,3102325248,
%T A016307 31113951232,311683706880,3120102240256,31220613439488,
%U A016307 312323680632832,3123942083788800,31243652502716416,312461915016265728,3124771490097528832,31248628940585041920
%N A016307 Expansion of g.f. 1/((1-2*x)*(1-6*x)*(1-10*x)).
%H A016307 Vincenzo Librandi, <a href="/A016307/b016307.txt">Table of n, a(n) for n = 0..500</a>
%H A016307 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-92,120).
%F A016307 From _Vincenzo Librandi_, Sep 01 2011: (Start)
%F A016307 a(n) = (2^n - 18*6^n + 25*10^n)/8.
%F A016307 a(n) = 18*a(n-1) - 92*a(n-2) + 120*a(n-3) for n > 2.
%F A016307 a(n) = 16*a(n-1) - 60*a(n-2) + 2^n for n > 1. (End)
%F A016307 From _Seiichi Manyama_, May 04 2025: (Start)
%F A016307 a(n) = Sum_{k=0..n} 4^k * 2^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).
%F A016307 a(n) = Sum_{k=0..n} (-4)^k * 10^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2). (End)
%F A016307 E.g.f.: exp(2*x)*(1 - 18*exp(4*x) + 25*exp(8*x))/8. - _Stefano Spezia_, May 04 2025
%t A016307 CoefficientList[Series[1/((1-2x)(1-6x)(1-10x)),{x,0,30}],x] (* or *) LinearRecurrence[{18,-92,120},{1,18,232},30] (* _Harvey P. Dale_, Nov 06 2019 *)
%o A016307 (Magma) [(2^n-18*6^n+25*10^n)/8: n in [0..20]]; // _Vincenzo Librandi_, Sep 01 2011
%Y A016307 Cf. A016297, A016315.
%K A016307 nonn,easy
%O A016307 0,2
%A A016307 _N. J. A. Sloane_