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Search: id:A159607
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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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+0
3
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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; listen)
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OFFSET
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0,3
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FORMULA
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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
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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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PROGRAM
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(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
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Cf. variants: A159606, A159608.
Sequence in context: A141625 A053588 A035352 this_sequence A087018 A005119 A090135
Adjacent sequences: A159604 A159605 A159606 this_sequence A159608 A159609 A159610
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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), May 16 2009
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