cp's OEIS Frontend

A081897 Fourth binomial transform of binomial(n+3, 3).

%I A081897 #19 Mar 22 2025 12:35:37
%S A081897 1,8,58,396,2595,16500,102500,625000,3753125,22250000,130468750,
%T A081897 757812500,4365234375,24960937500,141796875000,800781250000,
%U A081897 4498291015625,25146484375000,139953613281250,775756835937500,4283905029296875,23574829101562500,129318237304687500,707244873046875000
%N A081897 Fourth binomial transform of binomial(n+3, 3).
%C A081897 Binomial transform of A081895.
%C A081897 5th binomial transform of (1,3,3,1,0,0,0,0,...).
%H A081897 G. C. Greubel, <a href="/A081897/b081897.txt">Table of n, a(n) for n = 0..1000</a>
%H A081897 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (20,-150,500,-625)
%F A081897 a(n) = 5^n*(n^3 + 42*n^2 + 407*n + 750)/750.
%F A081897 G.f.: (1 - 4*x)^3/(1 - 5*x)^4.
%F A081897 E.g.f.: (6 + 18*x + 9*x^2 + x^3)*exp(5*x)/6. - _G. C. Greubel_, Oct 18 2018
%t A081897 LinearRecurrence[{20, -150, 500, -625}, {1, 8, 58, 396}, 50] (* _G. C. Greubel_, Oct 18 2018 *)
%o A081897 (PARI) x='x+O('x^30); Vec((1-4*x)^3/(1-5*x)^4) \\ _G. C. Greubel_, Oct 18 2018
%o A081897 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-4*x)^3/(1-5*x)^4)); // _G. C. Greubel_, Oct 18 2018
%Y A081897 Cf. A000292, A081895.
%K A081897 nonn,easy
%O A081897 0,2
%A A081897 _Paul Barry_, Mar 30 2003