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 A081902 #18 Mar 22 2025 13:30:21
%S A081902 1,9,66,434,2661,15525,87240,475920,2534400,13227520,67866624,
%T A081902 343105536,1712390144,8449622016,41273524224,199782039552,
%U A081902 959119884288,4570314964992,21629992173568,101729521631232,475697692803072,2212565287436288,10240198466076672,47175439742926848
%N A081902 Third binomial transform of binomial(n+5, 5).
%C A081902 Binomial transform of A081901.
%C A081902 4th binomial transform of (1,5,10,10,5,1,0,0,0,...).
%H A081902 G. C. Greubel, <a href="/A081902/b081902.txt">Table of n, a(n) for n = 0..1000</a>
%H A081902 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (24,-240,1280,-3840,6144,-4096).
%F A081902 a(n) = 4^n*(n^5 + 90*n^4 + 2635*n^3 + 29850*n^2 + 121024*n + 122880)/122880.
%F A081902 G.f.: (1 - 3*x)^5/(1 - 4*x)^6.
%F A081902 E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(4*x)/120. - _G. C. Greubel_, Oct 18 2018
%t A081902 LinearRecurrence[{24, -240, 1280, -3840, 6144, -4096}, {1, 9, 66, 434, 2661, 15525}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%t A081902 CoefficientList[Series[(1-3x)^5/(1-4x)^6,{x,0,30}],x] (* _Harvey P. Dale_, Apr 01 2023 *)
%o A081902 (PARI) x='x+O('x^30); Vec((1-3*x)^5/(1-4*x)^6) \\ _G. C. Greubel_, Oct 18 2018
%o A081902 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^5/(1-4*x)^6)); // _G. C. Greubel_, Oct 18 2018
%Y A081902 Cf. A000389, A081901, A081903.
%K A081902 nonn,easy
%O A081902 0,2
%A A081902 _Paul Barry_, Mar 31 2003