A258902 E.g.f.: Series_Reversion(x - x^2/2 - x^3/3).

1, 1, 5, 35, 355, 4585, 72485, 1353275, 29150275, 711535825, 19409915525, 585181872275, 19321831403875, 693431767653625, 26876449852377125, 1118833620294264875, 49786969727179559875, 2358371859530852790625, 118483568521991801253125, 6292649927564072269071875

Offset

1,3

Links

Table of n, a(n) for n=1..20.

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

Sequence in context: A360611 A201367 A233860 * A371028 A125864 A210996

Adjacent sequences: A258899 A258900 A258901 * A258903 A258904 A258905

Keyword

nonn

Author

Paul D. Hanna, Jun 14 2015

Status

approved