A177179 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)=9, k=1 and l=-1.

1, 9, 19, 121, 587, 3717, 22603, 149065, 988291, 6762757, 46812915, 329336265, 2340489211, 16803807621, 121604988955, 886446236169, 6501729726195, 47952147336325, 355387114288451, 2645435985621257, 19769671436457963

Offset: 0

Author

Richard Choulet, May 04 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*9+2-1=19. a(3)=2*1*19+2+81+1-1=121.
		

Crossrefs

Cf. A177178.

Programs

Maple

l:=-1: : k := 1 : m:=9: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) +(-17*n+43)*a(n-2) +(79*n-242)*a(n-3) +4*(-22*n+89)*a(n-4) +32*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016