cp's OEIS Frontend

A081893 Third binomial transform of C(n+2,2).

%I A081893 #14 Sep 08 2022 08:45:09
%S A081893 1,6,33,172,864,4224,20224,95232,442368,2031616,9240576,41680896,
%T A081893 186646528,830472192,3674210304,16173236224,70866960384,309237645312,
%U A081893 1344324763648,5823975653376,25151328485376,108301895335936
%N A081893 Third binomial transform of C(n+2,2).
%C A081893 Binomial transform of A081892.
%C A081893 3rd binomial transform of C(n+2,2), A000217.
%C A081893 4th binomial transform of (1,2,1,0,0,0,.....)
%H A081893 G. C. Greubel, <a href="/A081893/b081893.txt">Table of n, a(n) for n = 0..1000</a>
%H A081893 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-48,64).
%F A081893 a(n) = 4^n*(n^2 + 15*n + 32)/32.
%F A081893 G.f.: (1 - 3*x)^2/(1 - 4*x)^3.
%F A081893 E.g.f.: (2 + 4*x + x^2)*exp(4*x)/2. - _G. C. Greubel_, Oct 18 2018
%t A081893 LinearRecurrence[{12, -48, 64}, {1, 6, 33}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o A081893 (PARI) x='x+O('x^30); Vec((1-3*x)^2/(1-4*x)^3) \\ _G. C. Greubel_, Oct 18 2018
%o A081893 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-3*x)^2/(1-4*x)^3)); // _G. C. Greubel_, Oct 18 2018
%Y A081893 Cf. A081894.
%K A081893 nonn,easy
%O A081893 0,2
%A A081893 _Paul Barry_, Mar 30 2003