A176759 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)=0, k=1 and l=-1.

1, 0, 1, 4, 11, 27, 67, 178, 505, 1489, 4473, 13593, 41749, 129579, 406021, 1282464, 4077987, 13041655, 41919347, 135352451, 438827223, 1427986281, 4662359911, 15268900019, 50143755435, 165095296125, 544847069819, 1802020334105

Offset: 0

Author

Richard Choulet, Apr 25 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*0+2-1=1. a(3)=2*1*1+2+0^2+1-1=4. a(4)=2*1*4+2+2*0*1+2-1=11.
		

Crossrefs

Cf. A176757.

Programs

Maple

l:=-1: : k := 1 : m:=0: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=1, l=-1).

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +(-29*n+82)*a(n-3) +4*(5*n-19)*a(n-4) +4*(-n+5)*a(n-5)=0. - R. J. Mathar, Feb 18 2016