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%I #16 Oct 22 2024 15:17:44
%S 1,8,49,262,1286,5944,26262,111996,464103,1877904,7446735,29021490,
%T 111405780,422003520,1579757580,5851519704,21468622077,78087814776,
%U 281798184573,1009617794334,3593281988754,12710491403112,44705999907666
%N A sequence related to binomial(n+5, 5).
%C Binomial transform of A055852.
%C 2nd binomial transform of binomial(n+5, 5).
%C 3rd binomial transform of (1,5,10,10,5,1,0,0,0,...).
%H G. C. Greubel, <a href="/A081901/b081901.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-135,540,-1215,1458,-729).
%F a(n) = 3^n*(n^5 + 65*n^4 + 1385*n^3 + 11575*n^2 + 35574*n + 29160)/29160.
%F G.f.: (1 - 2*x)^5/(1 - 3*x)^6.
%F 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 LinearRecurrence[{18, -135, 540, -1215, 1458, -729}, {1, 8, 49, 262, 1286, 5944}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%t CoefficientList[Series[(1-2x)^5/(1-3x)^6,{x,0,30}],x] (* _Harvey P. Dale_, Oct 22 2024 *)
%o (PARI) x='x+O('x^30); Vec((1-2*x)^5/(1-3*x)^6) \\ _G. C. Greubel_, Oct 18 2018
%o (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 Cf. A081902.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 31 2003