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%I #4 Mar 30 2012 18:36:40
%S 1,1,3,11,44,185,802,3553,15994,72886,335387,1555487,7261310,34083382,
%T 160730900,761039051,3616102911,17235223345,82372594183,394648349447,
%U 1894921311499,9116598414141,43939539520427,212124129983285
%N G.f. A(x) satisfies xA(x)^5 = B(xA(x^5)) where B(x) = x/(1-5x).
%C More generally, given A(x) satisfies xA(x)^p = B(xA(x^p)) where B(x) = x/(1-p*x), then it appears that A(x) is an integer series only when p is prime. This is a special case of sequences with g.f.s that satisfy the more general functional equation xA(x)^m = B(xA(x^m)) originated by Michael Somos; some other examples are A085748, A091188 and A091190.
%o (PARI) {a(n)=local(A,m); p=5;if(n<0,0,m=1; A=1+O(x); while(m<=n,m*=p; A=x*subst(A,x,x^p); A=(A/(1-p*A)/x)^(1/p));polcoeff(A,n))}
%Y Cf. A085748, A091188, A091190.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Feb 23 2004
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