A177199 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, 15, 92, 421, 2535, 14561, 90770, 568023, 3668869, 23962891, 159056633, 1066354423, 7222075575, 49299161087, 338967663280, 2344974625813, 16312100074467, 114021548709433, 800494865098307, 5641966696544221

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) +3*(25*n-78)*a(n-3) +84*(-n+4)*a(n-4) +28*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

Example

a(2)=2*1*8-2+1=15. a(3)=2*1*15-2+64-1+1=92.

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

Sequence in context: A015442 A253211 A275246 * A177165 A189003 A110294

Adjacent sequences: A177196 A177197 A177198 * A177200 A177201 A177202

Keyword

easy,nonn

Author

Richard Choulet, May 04 2010

Status

approved