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A073398 Ninth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.

%I A073398 #13 Oct 07 2022 05:32:39
%S A073398 1,20,240,2200,16940,115104,711040,4072640,21930480,112157760,
%T A073398 549010176,2587777920,11802273600,52287866880,225756241920,
%U A073398 952486588416,3935984616960,15961485957120,63628396339200,249702113464320,965924035135488,3687247950397440
%N A073398 Ninth convolution of A002605(n) (generalized (2,2)-Fibonacci), n>=0, with itself.
%C A073398 For a(n) in terms of U(n+1) and U(n), with U(n) = A002605(n), see A073387 and the row polynomials of triangles A073405 and A073406.
%H A073398 G. C. Greubel, <a href="/A073398/b073398.txt">Table of n, a(n) for n = 0..1000</a>
%H A073398 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (20,-160,600,-660,-2496,7680,1920,-28320,7040, 66560,-14080,-113280,-15360,122880,79872,-42240,-76800,-40960,-10240,-1024).
%F A073398 a(n) = Sum_{k=0..n} b(k)*c(n-k), with b(k) = A002605(k) and c(k) = A073397(k).
%F A073398 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+9, 9)*binomial(n-k, k)*2^(n-k).
%F A073398 G.f.: 1/(1-2*x*(1+x))^10.
%t A073398 CoefficientList[Series[1/(1-2*x-2*x^2)^10, {x,0,30}], x] (* _G. C. Greubel_, Oct 06 2022 *)
%o A073398 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^10 )); // _G. C. Greubel_, Oct 06 2022
%o A073398 (SageMath)
%o A073398 def A073398_list(prec):
%o A073398     P.<x> = PowerSeriesRing(ZZ, prec)
%o A073398     return P( 1/(1-2*x-2*x^2)^10 ).list()
%o A073398 A073398_list(30) # _G. C. Greubel_, Oct 06 2022
%Y A073398 Tenth (m=9) column of triangle A073387.
%Y A073398 Cf. A002605, A073397, A073405, A073406.
%K A073398 nonn,easy
%O A073398 0,2
%A A073398 _Wolfdieter Lang_, Aug 02 2002