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

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

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

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 -+...

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)}

Crossrefs

Cf. variants: A159607, A159608.

Cf. A238223.

Sequence in context: A042437 A324514 A334786 * A211210 A177402 A036244

Adjacent sequences: A159603 A159604 A159605 * A159607 A159608 A159609

Keyword

sign

Author

Paul D. Hanna, May 16 2009

Status

approved