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Search: id:A107100
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| A107100 |
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Numerators of coefficients in g.f. that satisfies: [x^n] A(x)^(1/n) = 0 for all n>1, with a(0)=a(1)=1. |
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+0
2
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| 1, 1, 1, -1, -19, 17831, -64667, 1752946877, 796654376069593, -1318782726516512640001, 3482456481351141439684019, -6944717442120502790179764362411651, 32108006354107989164763518257678603933
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Sum_{n>=0} a(n) = 2.228747823105104822448312609661581467237449142548497707333713...
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EXAMPLE
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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, ...}.
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PROGRAM
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(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); numerator(polcoeff(A, n))}
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CROSSREFS
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Cf. A107101.
Sequence in context: A124989 A093400 A110392 this_sequence A125043 A068734 A034207
Adjacent sequences: A107097 A107098 A107099 this_sequence A107101 A107102 A107103
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KEYWORD
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frac,sign
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), May 12 2005
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