OFFSET
1,3
FORMULA
E.g.f. satisfies: A(x) = Integral 1/(1 - A(x) - A(x)^2) dx.
a(n) ~ 12^(n-1/2) * n^(n-1) / (5^(1/4) * exp(n) * (5*sqrt(5)-7)^(n-1/2)). - Vaclav Kotesovec, Jun 15 2015
Conjecture: +19*a(n) +21*(-2*n+3)*a(n-1) -4*(3*n-5)*(3*n-7)*a(n-2)=0. - R. J. Mathar, Jun 07 2016
EXAMPLE
E.g.f.: A(x) = x + x^2/2! + 5*x^3/3! + 35*x^4/4! + 355*x^5/5! + 4585*x^6/6! +...
where A(x - x^2/2 - x^3/3) = x.
MATHEMATICA
Rest[CoefficientList[InverseSeries[Series[x - x^2/2 - x^3/3, {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jun 15 2015 *)
PROG
(PARI) {a(n) = local(A=x); A = serreverse(x - x^2/2 - x^3/3 + x*O(x^n)); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) {a(n) = local(A=x); for(i=1, n, A = intformal(1/(1 - A - A^2 + x*O(x^n)))); n!*polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 14 2015
STATUS
approved