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A171443 Expansion of g.f. (1+x)^8/(1-x).

%I A171443 #31 Mar 19 2023 09:47:40
%S A171443 1,9,37,93,163,219,247,255,256,256,256,256,256,256,256,256,256,256,
%T A171443 256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,
%U A171443 256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256,256
%N A171443 Expansion of g.f. (1+x)^8/(1-x).
%C A171443 a(n)=2^8=256 for n>=8. We observe that this sequence is the transform of A171442 by T such that: T(u_0,u_1,u_2,u_3,u_4,u_5,...)=(u_0,u_0+u_1,u_1+u_2,u_2+u_3,u_3+u_4,...).
%H A171443 Vincenzo Librandi, <a href="/A171443/b171443.txt">Table of n, a(n) for n = 0..1000</a>
%H A171443 Richard Choulet, <a href="https://mp.sbpm.be/MP157.PDF">Une nouvelle formule de combinatoire?</a>, Mathématique et Pédagogie, 157 (2006), p. 53-60. In French.
%H A171443 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A171443 With m=9, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
%e A171443 a(7) = C(9,7-0)+C(9,7-2)+C(9,7-4)+C(9,7-6) = 36+126+84+9 = 255.
%p A171443 m:=9:for n from 0 to 40 do a(n):=sum('binomial(m,n-2*k)',k=0..floor(n/2)): od : seq(a(n),n=0..40);
%t A171443 CoefficientList[Series[(1+x)^8/(1-x),{x,0,80}],x] (* _Harvey P. Dale_, Jul 22 2014 *)
%Y A171443 Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171442.
%K A171443 nonn,easy
%O A171443 0,2
%A A171443 _Richard Choulet_, Dec 09 2009
%E A171443 Definition rewritten by _Bruno Berselli_, Sep 23 2011