A177182 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, 11, 67, 283, 1619, 8667, 50707, 296283, 1790163, 10921563, 67745043, 424241371, 2684071891, 17112955099, 109899184403, 710063310427, 4612990492883, 30113345315163, 197433924622099, 1299499526756827

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) +9*(-n+3)*a(n-2) +(71*n-226)*a(n-3) +4*(-22*n+89)*a(n-4) +32*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*7-2-1=11. a(3)=2*1*11-2+49-1-1=67.

Maple

l:=-1: : k := -1 : m:=7: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. A177181.

Sequence in context: A067690 A358585 A196181 * A061809 A289286 A337099

Adjacent sequences: A177179 A177180 A177181 * A177183 A177184 A177185

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved