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%I #15 Apr 01 2023 10:36:14
%S 1,9,66,434,2661,15525,87240,475920,2534400,13227520,67866624,
%T 343105536,1712390144,8449622016,41273524224,199782039552,
%U 959119884288,4570314964992,21629992173568,101729521631232,475697692803072
%N A sequence related to binomial(n+5, 5).
%C Binomial transform of A081901.
%C 3rd binomial transform of binomial(n+5, 5).
%C 4th binomial transform of (1,5,10,10,5,1,0,0,0,...).
%H G. C. Greubel, <a href="/A081902/b081902.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 (24,-240,1280,-3840,6144,-4096).
%F a(n) = 4^n*(n^5 + 90*n^4 + 2635*n^3 + 29850*n^2 + 121024*n + 122880)/122880.
%F G.f.: (1 - 3*x)^5/(1 - 4*x)^6.
%F 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 LinearRecurrence[{24, -240, 1280, -3840, 6144, -4096}, {1, 9, 66, 434, 2661, 15525}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%t CoefficientList[Series[(1-3x)^5/(1-4x)^6,{x,0,30}],x] (* _Harvey P. Dale_, Apr 01 2023 *)
%o (PARI) x='x+O('x^30); Vec((1-3*x)^5/(1-4*x)^6) \\ _G. C. Greubel_, Oct 18 2018
%o (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 Cf. A081903.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 31 2003
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