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 A081590 #19 Jun 09 2025 10:39:22
%S A081590 1,19,145,595,1585,3331,6049,9955,15265,22195,30961,41779,54865,70435,
%T A081590 88705,109891,134209,161875,193105,228115,267121,310339,357985,410275,
%U A081590 467425,529651,597169,670195,748945,833635,924481,1021699,1125505,1236115,1353745,1478611
%N A081590 Fourth row of Pascal-(1,5,1) array A081580.
%H A081590 Vincenzo Librandi, <a href="/A081590/b081590.txt">Table of n, a(n) for n = 0..10000</a>
%H A081590 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A081590 a(n) = 1 + 36*n - 54*n^2 + 36*n^3.
%F A081590 G.f.: (1+5*x)^3/(1-x)^4.
%F A081590 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=19, a(2)=145, a(3)=595. - _Harvey P. Dale_, Sep 07 2011
%F A081590 E.g.f.: exp(x)*(1 + 18*x + 54*x^2 + 36*x^3). - _Elmo R. Oliveira_, Jun 06 2025
%t A081590 Table[36n^3-54n^2+36n+1,{n,0,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{1,19,145,595},50] (* _Harvey P. Dale_, Sep 07 2011 *)
%o A081590 (Magma) [1+36*n-54*n^2+36*n^3: n in [0..40]]; // _Vincenzo Librandi_, Sep 07 2011
%Y A081590 Cf. A081580, A081589.
%K A081590 easy,nonn
%O A081590 0,2
%A A081590 _Paul Barry_, Mar 23 2003