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 A159606 G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x/A(x)). 4

%I

%S 1,1,-3,16,-115,996,-9870,108816,-1312227,17116900,-239641798,

%T 3580451040,-56837970358,955277226736,-16948413979080,316615678469856,

%U -6213840704926947,127857371413743540,-2753054722318717950

%N G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x/A(x)).

%H Vaclav Kotesovec, <a href="/A159606/b159606.txt">Table of n, a(n) for n = 0..400</a>

%F G.f. satisfies: x^2*A'(x) = 2*x*A(x) + (1-x)*A(x)^2 - A(x)^3.

%F a(n) ~ -(-1)^n * c * n! * n^3, where c = A238223 / exp(1) = 0.080179614624692622... - _Vaclav Kotesovec_, Nov 17 2017

%e G.f.: A(x) = 1 + x - 3*x^2 + 16*x^3 - 115*x^4 + 996*x^5 -+...

%e 1/A(x) = 1 - x + 4*x^2 - 23*x^3 + 166*x^4 - 1410*x^5 + 13602*x^6 -+...

%e log(1+x/A(x)) = x - 3*x^2/2 + 16*x^3/3 - 115*x^4/4 + 996*x^5/5 -+...

%o (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 Cf. variants: A159607, A159608.

%Y Cf. A238223.

%K sign

%O 0,3

%A _Paul D. Hanna_, May 16 2009

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Last modified December 5 09:03 EST 2020. Contains 338944 sequences. (Running on oeis4.)