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%I #4 Mar 30 2012 18:36:46
%S 1,1,4,54,4608,10800000,233280000,213462345600000,
%T 71945836874956800000,301100369020478344396800000,
%U 3345559655783092715520000000000,42953724653410633055099209541222400000000
%N Denominators of coefficients in g.f. that satisfies: [x^n] A(x)^(1/n) = 0 for all n>1, with a(0)=a(1)=1.
%F G.f. A(x) = Sum_{n>=0} A107100(n)/A107101(n)*x^n.
%e A(x) = 1 + x + 1/4*x^2 - 1/54*x^3 - 19/4608*x^4 +-...
%e A(x)^(1/2) = 1 + 1/2*x + 0*x^2 - 1/108*x^3 + 71/27648*x^4 -+...
%e A(x)^(1/3) = 1 + 1/3*x - 1/36*x^2 + 0*x^3 + 13/13824*x^4 -+...
%e A(x)^(1/4) = 1 + 1/4*x - 1/32*x^2 + 11/3456*x^3 + 0*x^4 -+...
%e Initial coefficients of A(x) are:
%e A107100/A107101 = {1, 1, 1/4, -1/54, -19/4608, 17831/10800000,
%e -64667/233280000, 1752946877/213462345600000,
%e 796654376069593/71945836874956800000,
%e -1318782726516512640001/301100369020478344396800000,
%e 3482456481351141439684019/3345559655783092715520000000000, ...}.
%o (PARI) {a(n)=local(A=1+x+x^2*O(x^n),C,D); for(k=2,n+1,C=polcoeff((A+t*x^k)^(1/k),k,x); D=(0-subst(C,t,0))/(subst(C,t,1)-subst(C,t,0));A=A+D*x^k); denominator(polcoeff(A,n))}
%Y Cf. A107100.
%K frac,nonn
%O 0,3
%A _Paul D. Hanna_, May 12 2005
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