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 A028025 #44 Feb 13 2025 08:26:44
%S A028025 1,18,205,1890,15421,116298,830845,5709330,38119741,249026778,
%T A028025 1599719485,10142356770,63639854461,396031348458,2448208592125,
%U A028025 15053605980210,92160458747581,562225198873338,3419937140824765
%N A028025 Expansion of 1/((1-3x)*(1-4x)*(1-5x)*(1-6x)).
%C A028025 This gives the fourth column of the Sheffer triangle A143495 (3-restricted Stirling2 numbers). See the e.g.f. given below, and comments on the general case under A193685. - _Wolfdieter Lang_, Oct 08 2011
%H A028025 Harvey P. Dale, <a href="/A028025/b028025.txt">Table of n, a(n) for n = 0..1000</a>
%H A028025 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (18,-119,342,-360).
%F A028025 If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,3), (n >= 3). - _Milan Janjic_, Apr 26 2009
%F A028025 a(n) = -5^(n+3)/2 + 2*4^(n+2)+ 6^(n+2) - 3^(n+2)/2. - _R. J. Mathar_, Mar 22 2011
%F A028025 O.g.f.: 1/((1-3*x)*(1-4*x)*(1-5*x)*(1-6*x)).
%F A028025 E.g.f.: (d^3/dx^3)(exp(3*x)*((exp(x)-1)^3)/3!). - _Wolfdieter Lang_, Oct 08 2011
%t A028025 CoefficientList[Series[1/((1-3x)(1-4x)(1-5x)(1-6x)),{x,0,30}],x] (* or *) LinearRecurrence[{18,-119,342,-360},{1,18,205,1890},30] (* _Harvey P. Dale_, Jan 29 2024 *)
%o A028025 (PARI) Vec(1/((1-3*x)*(1-4*x)*(1-5*x)*(1-6*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A028025 Cf. A000453, A025211, A003468, A028165, A028200, A016109, A016075, A016094.
%Y A028025 Cf. A143495, A193685.
%K A028025 nonn,easy
%O A028025 0,2
%A A028025 _N. J. A. Sloane_