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A107101
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.
2
1, 1, 4, 54, 4608, 10800000, 233280000, 213462345600000, 71945836874956800000, 301100369020478344396800000, 3345559655783092715520000000000, 42953724653410633055099209541222400000000
OFFSET
0,3
FORMULA
G.f. A(x) = Sum_{n>=0} A107100(n)/A107101(n)*x^n.
EXAMPLE
A(x) = 1 + x + 1/4*x^2 - 1/54*x^3 - 19/4608*x^4 +-...
A(x)^(1/2) = 1 + 1/2*x + 0*x^2 - 1/108*x^3 + 71/27648*x^4 -+...
A(x)^(1/3) = 1 + 1/3*x - 1/36*x^2 + 0*x^3 + 13/13824*x^4 -+...
A(x)^(1/4) = 1 + 1/4*x - 1/32*x^2 + 11/3456*x^3 + 0*x^4 -+...
Initial coefficients of A(x) are:
A107100/A107101 = {1, 1, 1/4, -1/54, -19/4608, 17831/10800000,
-64667/233280000, 1752946877/213462345600000,
796654376069593/71945836874956800000,
-1318782726516512640001/301100369020478344396800000,
3482456481351141439684019/3345559655783092715520000000000, ...}.
PROG
(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))}
CROSSREFS
Cf. A107100.
Sequence in context: A324235 A125531 A095209 * A147780 A361524 A140604
KEYWORD
frac,nonn
AUTHOR
Paul D. Hanna, May 12 2005
STATUS
approved