A176612 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)=2, k=1 and l=1.

1, 2, 7, 22, 77, 297, 1217, 5192, 22807, 102427, 468067, 2169227, 10170687, 48155437, 229916207, 1105682842, 5350944837, 26040130117, 127349649297, 625556921097, 3085016483557, 15268791946687, 75816909660597

Offset: 0

Author

Richard Choulet, Apr 21 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*2+2+1=7. a(3)=2*1*7+2+2^2+1+1=22. a(4)=2*1*22+2+2*2*7+2+1=77.
		

Crossrefs

Cf. A176611.

Programs

Maple

l:=1: : k := 1 : m :=2: 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

Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +(-13*n+38)*a(n-3) +12*(n-4)*a(n-4) +4*(-n+5)*a(n-5)=0. - R. J. Mathar, Feb 29 2016