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 A190050 #15 Jun 02 2025 04:04:38
%S A190050 1,2,6,17,46,120,304,752,1824,4352,10240,23808,54784,124928,282624,
%T A190050 634880,1417216,3145728,6946816,15269888,33423360,72876032,158334976,
%U A190050 342884352,740294656,1593835520,3422552064
%N A190050 Expansion of ((1-x)*(3*x^2-3*x+1))/(1-2*x)^3.
%C A190050 The second left hand column of triangle A175136.
%H A190050 G. C. Greubel, <a href="/A190050/b190050.txt">Table of n, a(n) for n = 0..1000</a>
%H A190050 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F A190050 G.f.: ((1-x)*(3*x^2-3*x+1))/(1-2*x)^3.
%F A190050 a(n) = (n^2 + 5*n + 10)*2^(n-4) for n >=1 with a(0)=1.
%F A190050 a(n) = A001788(n+1) -4*A001788(n) +6*A001788(n-1) -3*A001788(n-2) for n >=1 with a(0)=1.
%p A190050 A190050:= proc(n) option remember; if n=0 then A190050(n):=1: else A190050(n):=(n^2+5*n+10)*2^(n-4) fi: end: seq (A190050(n), n=0..26);
%t A190050 Join[{1}, LinearRecurrence[{6,-12,8}, {2,6,17}, 30]] (* or *) CoefficientList[Series[((1-x)*(3*x^2-3*x+1))/(1-2*x)^3, {x, 0, 50}], x] (* _G. C. Greubel_, Jan 10 2018 *)
%o A190050 (PARI) x='x+O('x^30); Vec(((1-x)*(3*x^2-3*x+1))/(1-2*x)^3) \\ _G. C. Greubel_, Jan 10 2018
%o A190050 (PARI) for(n=0,30, print1(if(n==0,1,(n^2 + 5*n + 10)*2^(n-4)), ", ")) \\ _G. C. Greubel_, Jan 10 2018
%o A190050 (Magma) [1] cat [(n^2 + 5*n + 10)*2^(n-4): n in [1..30]]; // _G. C. Greubel_, Jan 10 2018
%Y A190050 Cf. A175136, A011782, A190951.
%Y A190050 Related to A001788.
%K A190050 nonn,easy
%O A190050 0,2
%A A190050 _Johannes W. Meijer_, May 06 2011