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A143139
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E.g.f.: A(x) = exp(x + A(x)^2) - 1.
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2
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1, 3, 25, 351, 6901, 174483, 5392465, 196967991, 8301682141, 396555037803, 21171512707225, 1249311005445231, 80742309245690821, 5672134436846492163, 430345858647623635105, 35069095795843414698471
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| E.g.f. derivative: A'(x) = (1 + A(x))/(1 - 2*A(x) - 2*A(x)^2 ).
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EXAMPLE
| A(x) = x + 3*x^2/2! + 25*x^3/3! + 351*x^4/4! + 6901*x^5/5! +...
Log(1 + A(x)) = x + A(x)^2 = G(x) = g.f. of A143138:
G(x) = x + 2*x^2/2! + 18*x^3/3! + 254*x^4/4! + 5010*x^5/5! +...
A(x)^2 = 2*x^2/2! + 18*x^3/3! + 254*x^4/4! + 5010*x^5/5! +...
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PROG
| (PARI) {a(n)=local(A=x+O(x^n)); for(i=0, n, A=exp(x+A^2)-1); n!*polcoeff(A, n)}
(PARI) {a(n)=n!*polcoeff(exp(serreverse(x-(exp(x+x*O(x^n))-1)^2))-1, n)}
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CROSSREFS
| Cf. A143138.
Sequence in context: A093360 A161629 A129506 * A012481 A132617 A192552
Adjacent sequences: A143136 A143137 A143138 * A143140 A143141 A143142
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2008
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