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 A081901 #19 Mar 22 2025 13:30:07
%S A081901 1,8,49,262,1286,5944,26262,111996,464103,1877904,7446735,29021490,
%T A081901 111405780,422003520,1579757580,5851519704,21468622077,78087814776,
%U A081901 281798184573,1009617794334,3593281988754,12710491403112,44705999907666,156414048864948,544562500963779,1887215083472448
%N A081901 Second binomial transform of binomial(n+5, 5).
%C A081901 Binomial transform of A055852 (without leading 0).
%C A081901 3rd binomial transform of (1,5,10,10,5,1,0,0,0,...).
%H A081901 G. C. Greubel, <a href="/A081901/b081901.txt">Table of n, a(n) for n = 0..1000</a>
%H A081901 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-135,540,-1215,1458,-729).
%F A081901 a(n) = 3^n*(n^5 + 65*n^4 + 1385*n^3 + 11575*n^2 + 35574*n + 29160)/29160.
%F A081901 G.f.: (1 - 2*x)^5/(1 - 3*x)^6.
%F A081901 E.g.f.: (120 + 600*x + 600*x^2 + 200*x^3 + 25*x^4 + x^5)*exp(3*x)/120. - _G. C. Greubel_, Oct 18 2018
%t A081901 LinearRecurrence[{18, -135, 540, -1215, 1458, -729}, {1, 8, 49, 262, 1286, 5944}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%t A081901 CoefficientList[Series[(1-2x)^5/(1-3x)^6,{x,0,30}],x] (* _Harvey P. Dale_, Oct 22 2024 *)
%o A081901 (PARI) x='x+O('x^30); Vec((1-2*x)^5/(1-3*x)^6) \\ _G. C. Greubel_, Oct 18 2018
%o A081901 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^5/(1-3*x)^6)); // _G. C. Greubel_, Oct 18 2018
%Y A081901 Cf. A000389, A055852, A081902.
%K A081901 nonn,easy
%O A081901 0,2
%A A081901 _Paul Barry_, Mar 31 2003