A177168 Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=6, k=0 and l=-2.

1, 6, 10, 54, 226, 1198, 6186, 34182, 190962, 1096286, 6377338, 37652278, 224654146, 1353562766, 8220739274, 50284009702, 309467901842, 1915015423678, 11907759661850, 74365628891286, 466240095217378, 2933473106737902

Offset: 0

Author

Richard Choulet, May 04 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*6-2=10. a(3)=2*1*10+36-2=54.
		

Crossrefs

Cf. A176757.

Programs

Maple

l:=-2: : k := 0 : m:=6:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);

Formula

G.f f: f(z)=(1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=0, l=-2).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-11*n+27)*a(n-2) +2*(22*n-69)*a(n-3) +28*(-n+4)*a(n-4)=0. - R. J. Mathar, Jun 14 2016