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 A081898 #18 Mar 22 2025 12:35:18
%S A081898 1,7,39,193,886,3858,16146,65502,259119,1003833,3820689,14322663,
%T A081898 52986636,193759452,701265924,2514778812,8943620589,31569189723,
%U A081898 110673119691,385569479997,1335567565746,4601780568342,15778086835014,53852222811978,183024799992891,619577180566893
%N A081898 Second binomial transform of binomial(n+4, 4).
%C A081898 Binomial transform of A055589 (without leading 0).
%C A081898 3rd binomial transform of (1,4,6,4,1,0,0,0,...).
%H A081898 G. C. Greubel, <a href="/A081898/b081898.txt">Table of n, a(n) for n = 0..1000</a>
%H A081898 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-90,270,-405,243).
%F A081898 a(n) = 3^n*(n^4 + 42*n^3 + 515*n^2 + 2034*n + 1944)/1944.
%F A081898 G.f.: (1 - 2*x)^4/(1 - 3*x)^5.
%F A081898 E.g.f.: (24 + 96*x + 72*x^2 + 16*x^3 + x^4)*exp(3*x)/24. - _G. C. Greubel_, Oct 18 2018
%t A081898 LinearRecurrence[{15,-90,270,-405,243}, {1,7,39,193,886}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o A081898 (PARI) x='x+O('x^30); Vec((1-2*x)^4/(1-3*x)^5) \\ _G. C. Greubel_, Oct 18 2018
%o A081898 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^4/(1-3*x)^5)); // _G. C. Greubel_, Oct 18 2018
%Y A081898 Cf. A000332, A055589, A081899.
%K A081898 nonn,easy
%O A081898 0,2
%A A081898 _Paul Barry_, Mar 30 2003