A177177 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)=7, k=1 and l=-1.

1, 7, 15, 81, 375, 2113, 11911, 71221, 433343, 2704049, 17125871, 110044549, 714925975, 4690166833, 31020995831, 206646565637, 1385159527343, 9335979423089, 63232378792703, 430146956724677, 2937659194003655

Offset: 0

Author

Richard Choulet, May 04 2010

Keywords

• easy
• nonn

Examples

			a(2)=2*1*7+2-1=15. a(3)=2*1*15+2+49+1-1=81.
		

Crossrefs

Cf. A177176.

Programs

Maple

l:=-1: : k := 1 : m:=5: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) +9*(-n+3)*a(n-2) +5*(11*n-34)*a(n-3) +4*(-16*n+65)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016