|
%I #15 Sep 08 2022 08:45:09
%S 1,5,22,90,351,1323,4860,17496,61965,216513,747954,2558790,8680203,
%T 29229255,97785144,325241892,1076168025,3544180029,11622614670,
%U 37967207922,123587135991,400980206115,1297083797172,4184141281200
%N Second binomial transform of C(n+2,2).
%C Binomial transform of A049611(n+1).
%C 2nd binomial transform of C(n+2,2), A000217.
%C 3rd binomial transform of (1,2,1,0,0,0,.....)
%H G. C. Greubel, <a href="/A081892/b081892.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-27,27).
%F a(n) = 3^(n - 2)*(n + 2)*(n + 9)/2 = 3^n*(n^2 + 11*n + 18)/18.
%F G.f.: (1 - 2*x)^2/(1 - 3*x)^3.
%F E.g.f.: (2 + 4*x + x^2)*exp(3*x)/2. - _G. C. Greubel_, Oct 18 2018
%t LinearRecurrence[{9, -27, 27}, {1, 5, 22}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o (PARI) x='x+O('x^30); Vec((1-2*x)^2/(1-3*x)^3) \\ _G. C. Greubel_, Oct 18 2018
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x)^2/(1-3*x)^3)); // _G. C. Greubel_, Oct 18 2018
%Y Cf. A081893.
%Y A right-edge column of triangle A024462.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Mar 30 2003
|
