cp's OEIS Frontend

A081894 Fourth binomial transform of C(n+2,2).

%I A081894 #12 Sep 08 2022 08:45:09
%S A081894 1,7,46,290,1775,10625,62500,362500,2078125,11796875,66406250,
%T A081894 371093750,2060546875,11376953125,62500000000,341796875000,
%U A081894 1861572265625,10101318359375,54626464843750,294494628906250,1583099365234375
%N A081894 Fourth binomial transform of C(n+2,2).
%C A081894 Binomial transform of A081893.
%C A081894 4th binomial transform of C(n+2,2), A000217.
%C A081894 5th binomial transform of (1,2,1,0,0,0,.....)
%H A081894 G. C. Greubel, <a href="/A081894/b081894.txt">Table of n, a(n) for n = 0..1000</a>
%H A081894 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-75,125).
%F A081894 a(n) = 5^n*(n^2 + 19*n + 50)/50.
%F A081894 G.f.: (1 - 4*x)^2/(1 - 5*x)^3.
%F A081894 E.g.f.: (2 + 4*x + x^2)*exp(5*x)/2. - _G. C. Greubel_, Oct 18 2018
%t A081894 LinearRecurrence[{15, -75, 125}, {1, 7, 46}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o A081894 (PARI) x='x+O('x^30); Vec((1-4*x)^2/(1-5*x)^3) \\ _G. C. Greubel_, Oct 18 2018
%o A081894 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^2/(1-5*x)^3)); // _G. C. Greubel_, Oct 18 2018
%Y A081894 Cf. A081907.
%K A081894 nonn,easy
%O A081894 0,2
%A A081894 _Paul Barry_, Mar 30 2003