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Search: id:A143138
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| A143138 |
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E.g.f.: A(x) = x + (exp(A(x)) - 1)^2. |
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+0
3
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| 1, 2, 18, 254, 5010, 126902, 3926538, 143539454, 6053432130, 289293272102, 15450565342938, 911991586990574, 58955877533817810, 4142488437549926102, 314346159031755778218, 25620077133245941688414
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Radius of convergence is r = log((2+sqrt(3))/2)/2 - (2-sqrt(3))/2 = 0.17793076... where A(r) = log((sqrt(3)+1)/2) = 0.311905358...
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FORMULA
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E.g.f.: A(x) = Series_Reversion( x - (exp(x) - 1)^2 ).
E.g.f. derivative: A'(x) = 1/(1 + 2*exp(A(x)) - 2*exp(2*A(x)) ).
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EXAMPLE
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A(x) = x + 2*x^2/2! + 18*x^3/3! + 254*x^4/4! + 5010*x^5/5! +...
exp(A(x)) - 1 = G(x) = the g.f. of A143139:
G(x) = x + 3*x^2/2! + 25*x^3/3! + 351*x^4/4! + 6901*x^5/5! +...
G(x)^2 = 2*x^2/2! + 18*x^3/3! + 254*x^4/4! + 5010*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=local(A=x+O(x^n)); for(i=0, n, A=x + (exp(A)-1)^2); n!*polcoeff(A, n)}
(PARI) {a(n)=n!*polcoeff(serreverse(x-(exp(x+x*O(x^n))-1)^2), n)}
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CROSSREFS
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Cf. A143139.
Sequence in context: A138437 A121429 A109517 this_sequence A151362 A099880 A141009
Adjacent sequences: A143135 A143136 A143137 this_sequence A143139 A143140 A143141
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2008
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