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A159606
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G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x/A(x)).
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2
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1, 1, -3, 16, -115, 996, -9870, 108816, -1312227, 17116900, -239641798, 3580451040, -56837970358, 955277226736, -16948413979080, 316615678469856, -6213840704926947, 127857371413743540, -2753054722318717950
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| G.f. satisfies: x^2*A'(x) = 2*x*A(x) + (1-x)*A(x)^2 - A(x)^3.
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EXAMPLE
| G.f.: A(x) = 1 + x - 3*x^2 + 16*x^3 - 115*x^4 + 996*x^5 -+...
1/A(x) = 1 - x + 4*x^2 - 23*x^3 + 166*x^4 - 1410*x^5 + 13602*x^6 -+...
log(1+x/A(x)) = x - 3*x^2/2 + 16*x^3/3 - 115*x^4/4 + 996*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)^-1)+x*O(x^n))); polcoeff(A, n)}
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CROSSREFS
| Cf. variants: A159607, A159608.
Sequence in context: A124537 A074523 A042437 * A177402 A036244 A011818
Adjacent sequences: A159603 A159604 A159605 * A159607 A159608 A159609
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KEYWORD
| sign
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), May 16 2009
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