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A159607
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G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x*A(x)^2).
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2
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1, 1, 3, 16, 123, 1221, 14724, 207908, 3355803, 60873595, 1225319163, 27097430328, 653052022740, 17036213760892, 478306368143880, 14381009543824236, 461038595072589531, 15699544671941958663, 565927686301436324649
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f. satisfies: A(x) = 1 + x*A(x)^2*(2 - A(x)) + 2*x^2*A'(x)*A(x).
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EXAMPLE
| G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 123*x^4 + 1221*x^5 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 38*x^3 + 287*x^4 + 2784*x^5 +...
log(1+x*A(x)^2) = x + 3*x^2/2 + 16*x^3/3 + 123*x^4/4 + 1221*x^5/5 +...
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PROG
| (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(log(1+x*Ser(A)^2)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
| Cf. variants: A159606, A159608.
Sequence in context: A141625 A053588 A035352 * A087018 A005119 A190291
Adjacent sequences: A159604 A159605 A159606 * A159608 A159609 A159610
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 16 2009
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