A177126 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)=10, k=1 and l=1.

1, 10, 23, 150, 765, 5065, 32337, 223672, 1556583, 11178843, 81228819, 599868763, 4475307567, 33731219901, 256268778463, 1961208117130, 15101975890677, 116936866669157, 909887821312929, 7110983852617913, 55793178281433653

Offset: 0

Author

Richard Choulet, May 03 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*10+2+1=23. a(3)=2*1*23+2+10^2+1+1=150.
		

Crossrefs

Cf. A177125.

Programs

Maple

l:=1: : k := 1 : m :=10: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

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*(n+1)*a(n) -n*(7*n-2)*a(n-1) -3*n*(7*n-17)*a(n-2) +n*(83*n-250)*a(n-3) -84*n*(n-4)*a(n-4) +28*n*(n-5)*a(n-5) =0. - R. J. Mathar, Jul 24 2012