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 A383910 #18 May 15 2025 07:10:35
%S A383910 1,12,72,312,1152,3912,12672,39912,123552,378312,1150272,3481512,
%T A383910 10505952,31640712,95167872,285995112,858968352,2578871112,7740545472,
%U A383910 23229500712,69704230752,209144149512,627495363072,1882611918312,5648087413152,16944765555912,50835303300672
%N A383910 Expansion of Product_{k=0..3} (1 + k*x)/(1 - k*x).
%H A383910 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-11,6).
%F A383910 a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 3.
%F A383910 a(n) = Sum_{k=0..3} |Stirling1(4,k+1)| * Stirling2(k+n,3).
%F A383910 a(n) = A383912(n) + 3*A383912(n-1) = 20*3^n - 15*2^(n+1) + 12 = 10*A091344(n) + 2 for n > 0.
%o A383910 (PARI) a(n) = if(n==0, 1, 20*3^n-15*2^(n+1)+12);
%Y A383910 Column k=3 of A383900.
%Y A383910 Cf. A091344, A383912.
%K A383910 nonn,easy
%O A383910 0,2
%A A383910 _Seiichi Manyama_, May 14 2025