A177172 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=0 and l=-2.

1, 10, 18, 134, 626, 4254, 25850, 177270, 1192450, 8392846, 59270218, 427294630, 3103586514, 22805459262, 168767740698, 1258575706582, 9441189199010, 71224314198510, 539889535264490, 4110514381564422, 31418080601125746

Offset: 0

Author

Richard Choulet, May 04 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*10-2=18. a(3)=2*1*18+100-2=134.
		

Crossrefs

Cf. A177171.

Programs

Maple

l:=-2: : k := 0 : for m from 0 to 10 do d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p),p=0..n)-2: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): od;

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) +(-27*n+59)*a(n-2) +2*(38*n-117)*a(n-3) +44*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 21 2016