A177178 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=1 and l=-1.

1, 8, 17, 100, 475, 2843, 16691, 105026, 668777, 4379697, 29069769, 195897417, 1334255973, 9178287643, 63648492949, 444568586864, 3124500279731, 22080853944311, 156808387564259, 1118463885704019, 8009066218515015

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=1, l=-1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-13*n+35)*a(n-2) +(67*n-206)*a(n-3) +4*(-19*n+77)*a(n-4) +28*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*8+2-1=17. a(3)=2*1*17+2+64+1-1=100.

Maple

l:=-1: : k := 1 : 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. A177177.

Sequence in context: A134790 A350683 A177129 * A357678 A097405 A192282

Adjacent sequences: A177175 A177176 A177177 * A177179 A177180 A177181

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved