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 A021874 #35 May 03 2025 10:19:20
%S A021874 1,22,325,4070,46781,511742,5430405,56516790,580744461,5916830062,
%T A021874 59935396885,604729235110,6084941584541,61113049957982,
%U A021874 612976296281765,6142684971387030,61517309500479021,615806336417543502,6162496145690677045,61655991294017340550,616777123265962899901
%N A021874 Expansion of 1/((1-x) * (1-4*x) * (1-7*x) * (1-10*x)).
%H A021874 Vincenzo Librandi, <a href="/A021874/b021874.txt">Table of n, a(n) for n = 0..200</a>
%H A021874 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-159,418,-280).
%F A021874 a(n) = (10^(n+3) - 3*7^(n+3) + 3*4^(n+3) - 1)/162. - _Yahia Kahloune_, Jul 05 2013
%F A021874 E.g.f.: exp(x)*(1000*exp(9*x) - 1029*exp(6*x) + 192*exp(3*x) - 1)/(3!*3^3). This is d^3/dx^3 exp(x)*(exp(3*x - 1))^3/(3!*3^3); see also column m=3 of A282629 divided by 3^3. The o.g.f. is given in the name. - _Wolfdieter Lang_, Apr 08 2017
%F A021874 a(n) = Sum_{k=0..n} 3^k * binomial(n+3,k+3) * Stirling2(k+3,3). - _Seiichi Manyama_, May 03 2025
%t A021874 CoefficientList[Series[1 / ((1 - x) (1 - 4 x) (1 - 7 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 11 2013 *)
%t A021874 LinearRecurrence[{22,-159,418,-280},{1,22,325,4070},30] (* _Harvey P. Dale_, May 13 2018 *)
%Y A021874 Cf. A002450, A016223, A111577.
%Y A021874 Cf. A000012, A282629.
%K A021874 nonn,easy
%O A021874 0,2
%A A021874 _N. J. A. Sloane_