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 A081588 #13 Jun 09 2025 00:40:41
%S A081588 1,16,106,396,1011,2076,3716,6056,9221,13336,18526,24916,32631,41796,
%T A081588 52536,64976,79241,95456,113746,134236,157051,182316,210156,240696,
%U A081588 274061,310376,349766,392356,438271,487636,540576,597216,657681,722096,790586,863276,940291
%N A081588 Fourth row of the Pascal-(1,4,1) array A081579.
%H A081588 Vincenzo Librandi, <a href="/A081588/b081588.txt">Table of n, a(n) for n = 0..1000</a>
%H A081588 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A081588 a(n) = (6 + 115*n - 150*n^2 + 125*n^3)/6.
%F A081588 G.f.: (1+4*x)^3/(1-x)^4.
%F A081588 From _Elmo R. Oliveira_, Jun 06 2025: (Start)
%F A081588 E.g.f.: exp(x)*(6 + 90*x + 225*x^2 + 125*x^3)/6.
%F A081588 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)
%t A081588 CoefficientList[Series[(1 + 4 x)^3 / (1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 09 2013 *)
%o A081588 (Magma) [(6+115*n-150*n^2+125*n^3)/6: n in [0..40]]; // _Vincenzo Librandi_, Aug 09 2013
%Y A081588 Cf. A081579, A081587.
%K A081588 easy,nonn
%O A081588 0,2
%A A081588 _Paul Barry_, Mar 23 2003