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%I #14 Apr 27 2015 11:44:57
%S 1,1,1,1,2,5,15,51,191,773,3338,15243,73131,366815,1916260,10394665,
%T 58404853,339223859,2033188222,12556915219,79807729238,521399203037,
%U 3497978659977,24076009827669,169865542733652,1227553152971419,9079751310622581
%N G.f. satisfies: A(x) = 1+x + x^2*A( (A(x)-1-x)/x ).
%H Vaclav Kotesovec, <a href="/A193296/b193296.txt">Table of n, a(n) for n = 0..280</a>
%F G.f. satisfies: A(x/A(x)) = 1 + (1+x)*x/A(x).
%F G.f. satisfies: A(x) = 1+x + x*Series_Reversion(x/A(x)).
%F a(n) = [x^(n-2)] A(x)^(n-1)/(n-1) for n>=2 with a(0)=a(1)=1.
%e G.f.: A(x) = 1 + x + x^2 + x^3 + 2*x^4 + 5*x^5 + 15*x^6 + 51*x^7 +...
%e where
%e (A(x)-1-x)/x = x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 51*x^6 + 191*x^7 +...
%e A((A(x)-1-x)/x) = 1 + x + 2*x^2 + 5*x^3 + 15*x^4 + 51*x^5 + 191*x^6 +...
%e A(x)*A(x/A(x)) = 1 + 2*x + 2*x^2 + x^3 + 2*x^4 + 5*x^5 + 15*x^6 + 51*x^7 +...
%o (PARI) {a(n)=local(A=1+x);for(i=1,n-1,A=1+x+x*serreverse(x/A+O(x^n)));polcoeff(A,n)}
%K nonn
%O 0,5
%A _Paul D. Hanna_, Jul 21 2011
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