OFFSET
0,3
COMMENTS
Row sums of triangle A080245.
REFERENCES
I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, Exercise 2.7.12.(b).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..300
FORMULA
G.f.: (-1+x+sqrt(1+6*x+x^2))/x/4. - Vladeta Jovovic, Sep 27 2003
Conjecture: (n+1)*a(n) +3*(2*n-1)*a(n-1) +(n-2)*a(n-2)=0. - R. J. Mathar, Nov 26 2012
G.f.: 1 - x/(Q(0) + x) where Q(k) = 1 + k*(1+x) + x + x*(k+1)*(k+2)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Mar 14 2013
a(n) ~ (-1)^n * sqrt(4+3*sqrt(2)) * (3+2*sqrt(2))^n /(4*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 15 2013
G.f. A(x) satisfies: A(x) = (1 - 2*x*A(x)^2) / (1 - x). - Ilya Gutkovskiy, Jun 30 2020
MATHEMATICA
CoefficientList[Series[(-1 + x + Sqrt[1 + 6 x + x^2]) /x / 4, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
PROG
(PARI) x='x+O('x^66); Vec( (-1+x+sqrt(1+6*x+x^2))/x/4 ) \\ Joerg Arndt, Aug 15 2013
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Barry, Feb 13 2003
STATUS
approved