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%I #7 Jun 13 2015 00:51:37
%S 1,1,2,4,9,21,49,113,258,586,1329,3015,6845,15549,35330,80280,182413,
%T 414461,941669,2139477,4860898,11044006,25092157,57009871,129527609,
%U 294289401,668631458,1519143916,3451524785,7841931877,17817022873
%N Sum C(n,2k)F(k+1), k=0..floor(n/2).
%C Transform of F(n+1) under the mapping g(x)-> (1/(1-x))g(x^2/((1-x)^2). Binomial transform of 1,0,1,0,2,0,3,0,5,...
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2,1)
%F G.f.: (1-x)^3/(1-4x+5x^2-2x^3-x^4); a(n)=4a(n-1)-5a(n-2)+2a(n-3)+a(n-4); a(n)=sum{k=0..n, binomial(n, k)(F((k+2)/2)(1+(-1)^k)/2}.
%Y Cf. A000045.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Dec 20 2004
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