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G.f. f(x) = Sum_{n>=1} a(n)*x^n satisfies f(f(x)) = x*(1 + 4*x).
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%I #24 May 03 2024 12:12:51

%S 0,1,2,-4,16,-80,432,-2304,10944,-35328,-74112,2736384,-30853632,

%T 238663680,-1247457280,2201247744,32530722816,-320650199040,

%U 156266184704,18314630348800,-20667999748096,-3428200020508672

%N G.f. f(x) = Sum_{n>=1} a(n)*x^n satisfies f(f(x)) = x*(1 + 4*x).

%H Seiichi Manyama, <a href="/A027436/b027436.txt">Table of n, a(n) for n = 0..486</a>

%F a(n) = 4^(n-1) * A097088(n) / 2^A097089(n).

%F T(n,m) = if n=m then 1 else (binomial(m,n-m)*4^(n-m)-sum(i=m+1..n-1, T(n,i)*T(i,m)))/2. a(n) = T(n,1). - _Vladimir Kruchinin_, Nov 08 2011

%Y Cf. A097088, A097089.

%K sign

%O 0,3

%A _Jonathan Deane_

%E Added a(0)=0 (sum in title starts at a(1)), _Henry Bottomley_, Apr 20 2011