A168073 Expansion of 1 + 3*(1-x-sqrt(1-2*x-3*x^2))/2.

1, 0, 3, 3, 6, 12, 27, 63, 153, 381, 969, 2505, 6564, 17394, 46533, 125505, 340902, 931716, 2560401, 7070337, 19609146, 54597852, 152556057, 427642677, 1202289669, 3389281245, 9578183391, 27130207503, 77009455428, 219023318406, 624069834627, 1781228354487

Offset: 0

Author

Paul Barry, Nov 18 2009

Keywords

• easy
• nonn

Comments

Hankel transform is A168072. a(n+2)=3*A000106(n). Another variant is A168076.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A168055, A168049.

Cf. A000106, A168072, A168076.

Programs

Mathematica

CoefficientList[Series[1 + 3*(1 - x - Sqrt[1 - 2*x - 3*x^2])/2, {x, 0, 50}], x] (* G. C. Greubel, Jul 09 2016 *)

Formula

a(n) = 0^n+3*Sum_{k=0..floor((n-2)/2)} C(n-2,2k)*A000108(k).

D-finite with recurrence: a(n) = ((2*n-3)*a(n-1)+(3*n-9)*a(n-2))/n for n>=3, a(0)=1, a(1)=0, a(2)=3. - Sergei N. Gladkovskii, Jul 16 2012