OFFSET
0,4
COMMENTS
Hankel transform is A186196. Hankel transform of a(n+1) is (-2)^C(n+1,2).
FORMULA
D-finite with recurrence n*a(n) +(4*n-3)*a(n-1) +(13*n-33)*a(n-2) +18*(n-3)*a(n-3)=0. - R. J. Mathar, Feb 13 2015
From Peter Bala, Nov 08 2022: (Start)
O.g.f. A(x) = 1 + series reversion of x*(1 + x)/((1 - x)*(1 + 2*x)).
The g.f. satisfies the differential equation (1 + 4*x + 13*x^2 + 18*x^3)*A'(x) + (1 - 7*x)*A(x) + (2*x - 2) = 0 with A(0) = 1. Mathar's recurrence above follows from this. (End)
MATHEMATICA
CoefficientList[Series[(1+5x+Sqrt[1+2x+9x^2])/(2(1+2x)), {x, 0, 30}], x] (* Harvey P. Dale, Dec 17 2021 *)
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Barry, Feb 14 2011
STATUS
approved