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Search: id:A159608
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| A159608 |
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G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x*A(x)^3). |
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+0
3
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| 1, 1, 5, 46, 597, 9791, 191876, 4348394, 111561125, 3192096511, 100729014305, 3474750994936, 130094553648612, 5254546985647116, 227771218849108212, 10548385893161367506, 519835256567911242341, 27164324421130818956039
(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*(2 - A(x))*A(x)^3 + 3*x^2*A'(x)*A(x)^2.
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EXAMPLE
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G.f.: A(x) = 1 + x + 5*x^2 + 46*x^3 + 597*x^4 + 9791*x^5 +...
A(x)^3 = 1 + 3*x + 18*x^2 + 169*x^3 + 2157*x^4 + 34548*x^5 +...
log(1+x*A(x)^3) = x + 5*x^2/2 + 46*x^3/3 + 597*x^4/4 + 9791*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)^3)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
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Cf. variants: A159606, A159607.
Sequence in context: A127304 A112029 A058478 this_sequence A167559 A121631 A071214
Adjacent sequences: A159605 A159606 A159607 this_sequence A159609 A159610 A159611
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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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