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A073385 Eighth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself.

%I A073385 #28 Oct 03 2022 08:45:36
%S A073385 1,18,189,1500,9945,58014,307197,1507176,6950295,30443270,127666539,
%T A073385 515754252,2017069431,7667214570,28419251715,102997948704,
%U A073385 365832349542,1275914693196,4376992440590
%N A073385 Eighth convolution of A000129(n+1) (generalized (2,1)-Fibonacci, called Pell numbers), n>=0, with itself.
%C A073385 For a(n) in terms of U(n+1) and U(n) with U(n) = A000129(n+1) see the row polynomials of triangles A058402 and A058403 and the comment there.
%H A073385 G. C. Greubel, <a href="/A073385/b073385.txt">Table of n, a(n) for n = 0..1000</a>
%H A073385 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (18,-135,528,-1044,504,1764,-2448,-1422,3308,1422, -2448,-1764,504,1044,528,135,18,1).
%F A073385 a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A000129(k+1) and c(k) = A073384(k).
%F A073385 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k)*binomial(n-k+8, 8)*binomial(n-k, k).
%F A073385 G.f.: 1/(1-(2+x)*x)^9.
%F A073385 a(n) = F''''''''(n+9, 2)/8!, that is, 1/8! times the 8th derivative of the (n+9)-th Fibonacci polynomial evaluated at x=2. - _T. D. Noe_, Jan 19 2006
%t A073385 CoefficientList[Series[1/(1-(2+x)x)^9,{x,0,20}],x] (* _Harvey P. Dale_, Apr 26 2017 *)
%o A073385 (Sage) taylor( 1/(1-2*x-x^2)^9, x, 0,27).list() # _G. C. Greubel_, Oct 03 2022
%o A073385 (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( 1/(1-2*x-x^2)^9 )); // _G. C. Greubel_, Oct 03 2022
%Y A073385 Ninth (m=8) column of triangle A054456.
%Y A073385 Cf. A000129, A058402, A058403, A073384.
%K A073385 nonn,easy
%O A073385 0,2
%A A073385 _Wolfdieter Lang_, Aug 02 2002