A177165 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)=8, k=0 and l=-1.

1, 8, 15, 93, 425, 2562, 14713, 91816, 574949, 3717500, 24302981, 161482101, 1083710423, 7347323094, 50206521743, 345571827445, 2393196284537, 16665285532548, 116614759448605, 819577862448031, 5782666072184523

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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=-1).

Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-19*n+43)*a(n-2) +4*(14*n-43)*a(n-3) +32*(-n+4)*a(n-4)=0. - R. J. Mathar, Jun 14 2016

Example

a(2)=2*1*8-1=15. a(3)=2*1*15+64-1=93.

Maple

l:=-1: : k := 0 : m:=8: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);

Crossrefs

Cf. A177163.

Sequence in context: A253211 A275246 A177199 * A189003 A110294 A110459

Adjacent sequences: A177162 A177163 A177164 * A177166 A177167 A177168

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved