A159606 G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x/A(x)).
1, 1, -3, 16, -115, 996, -9870, 108816, -1312227, 17116900, -239641798, 3580451040, -56837970358, 955277226736, -16948413979080, 316615678469856, -6213840704926947, 127857371413743540, -2753054722318717950
Offset: 0
Keywords
Examples
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 -+...
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..400
Programs
-
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)}
Formula
G.f. satisfies: x^2*A'(x) = 2*x*A(x) + (1-x)*A(x)^2 - A(x)^3.
a(n) ~ -(-1)^n * c * n! * n^3, where c = A238223 / exp(1) = 0.080179614624692622... - Vaclav Kotesovec, Nov 17 2017