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Search: id:A144681
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| A144681 |
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E.g.f. satisfies: A(x/A(x)) = exp(x). |
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+0
4
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| 1, 1, 3, 22, 305, 6656, 204337, 8226436, 414585425, 25315924960, 1828704716801, 153433983789164, 14739472821255481, 1602471473448455104, 195300935112810494801, 26470100501608768436716
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OFFSET
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0,3
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FORMULA
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E.g.f. satisfies: A(x) = exp( x*A(log A(x)) ).
E.g.f: A(x) = G(2x)^(1/2) where G(x/G(x)^2) = exp(x) and G(x) is the e.g.f. of A144682.
E.g.f: A(x) = G(3x)^(1/3) where G(x/G(x)^3) = exp(x) and G(x) is the e.g.f. of A144683.
E.g.f: A(x) = G(4x)^(1/4) where G(x/G(x)^4) = exp(x) and G(x) is the e.g.f. of A144684.
E.g.f: A(x) = 1/G(-x) where G(x*G(x)) = exp(x) and G(x) is the e.g.f. of A087961.
E.g.f. A(log(A(x))) = log(A(x))/x = G(x) is the e.g.f of A140049 where G(x) satisfies G(x*exp(-x*G(x))) = exp(x*G(x)).
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EXAMPLE
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E.g.f. A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 305*x^4/4! +...
A(x/A(x)) = 1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! +...
1/A(x) = 1 + x - x^2/2! + 10*x^3/3! - 159*x^4/4! + 3816*x^5/5! -+...
A(log(A(x)) = 1 + x + 5*x^2/2! + 55*x^3/3! + 1005*x^4/4! + 26601*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(n=0, n, A=exp(serreverse(x/A))); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A144682, A144683, A144684, A087961, A140049.
Sequence in context: A122778 A108991 A119390 this_sequence A124567 A161967 A102223
Adjacent sequences: A144678 A144679 A144680 this_sequence A144682 A144683 A144684
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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), Sep 19 2008
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