A159607 G.f. satisfies: A(x) = 1 + x*d/dx log(1 + x*A(x)^2).

1, 1, 3, 16, 123, 1221, 14724, 207908, 3355803, 60873595, 1225319163, 27097430328, 653052022740, 17036213760892, 478306368143880, 14381009543824236, 461038595072589531, 15699544671941958663, 565927686301436324649

Offset

0,3

Links

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

Formula

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

a(n) ~ c * n! * 2^n, where c = 0.343014753433948245763329120820010283... - Vaclav Kotesovec, Feb 22 2014

Example

G.f.: A(x) = 1 + x + 3*x^2 + 16*x^3 + 123*x^4 + 1221*x^5 +...
A(x)^2 = 1 + 2*x + 7*x^2 + 38*x^3 + 287*x^4 + 2784*x^5 +...
log(1+x*A(x)^2) = x + 3*x^2/2 + 16*x^3/3 + 123*x^4/4 + 1221*x^5/5 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(log(1+x*Ser(A)^2)+x*O(x^n))); polcoeff(A, n)}

Crossrefs

Cf. variants: A159606, A159608.

Sequence in context: A053588 A295928 A035352 * A087018 A005119 A190291

Adjacent sequences: A159604 A159605 A159606 * A159608 A159609 A159610

Keyword

nonn

Author

Paul D. Hanna, May 16 2009

Status

approved