Search: id:A159606
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%I A159606
%S A159606 1,1,3,16,115,996,9870,108816,1312227,17116900,239641798,
%T A159606 3580451040,56837970358,955277226736,16948413979080,316615678469856,
%U A159606 6213840704926947,127857371413743540,2753054722318717950
%V A159606 1,1,-3,16,-115,996,-9870,108816,-1312227,17116900,-239641798,
%W A159606 3580451040,-56837970358,955277226736,-16948413979080,316615678469856,
%X A159606 -6213840704926947,127857371413743540,-2753054722318717950
%N A159606 G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x/A(x)).
%F A159606 G.f. satisfies: x^2*A'(x) = 2*x*A(x) + (1-x)*A(x)^2 - A(x)^3.
%e A159606 G.f.: A(x) = 1 + x - 3*x^2 + 16*x^3 - 115*x^4 + 996*x^5 -+...
%e A159606 1/A(x) = 1 - x + 4*x^2 - 23*x^3 + 166*x^4 - 1410*x^5 + 13602*x^6 -+...
%e A159606 log(1+x/A(x)) = x - 3*x^2/2 + 16*x^3/3 - 115*x^4/4 + 996*x^5/5 -+...
%o A159606 (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)}
%Y A159606 Cf. variants: A159607, A159608.
%Y A159606 Sequence in context: A124537 A074523 A042437 this_sequence A036244 A011818 
               A036248
%Y A159606 Adjacent sequences: A159603 A159604 A159605 this_sequence A159607 A159608 
               A159609
%K A159606 sign
%O A159606 0,3
%A A159606 Paul D. Hanna (pauldhanna(AT)juno.com), May 16 2009

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