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A171442 Expansion of (1+x)^7/(1-x).

%I A171442 #25 Mar 19 2023 10:41:26
%S A171442 1,8,29,64,99,120,127,128,128,128,128,128,128,128,128,128,128,128,128,
%T A171442 128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,
%U A171442 128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128,128
%N A171442 Expansion of (1+x)^7/(1-x).
%C A171442 a(n)=2^7=128 for n>=7. We observe that this sequence is the transform of A171441 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 A171442 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 A171442 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A171442 With m=8, a(n) = Sum_{k=0..floor(n/2)} binomial(m,n-2*k).
%e A171442 a(5) = C(8,5-0)+C(8,5-2)+C(8,5-4) = 56+56+8 = 120.
%p A171442 m:=8: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 A171442 CoefficientList[Series[(1+x)^7/(1-x),{x,0,60}],x] (* _Harvey P. Dale_, Apr 30 2012 *)
%Y A171442 Cf. A040000, A113311, A115291, A171418, A171440, A171441, A171443.
%K A171442 nonn,easy
%O A171442 0,2
%A A171442 _Richard Choulet_, Dec 09 2009
%E A171442 Definition rewritten by _Bruno Berselli_, Sep 23 2011