%I #11 Jan 30 2020 21:29:16

%S 1,0,-4,-14,-36,-66,-32,406,2332,8046,18472,13558,-127580,-848722,

%T -3236272,-8208026,-8089908,51660014,389206456,1588065494,4318743220,

%U 5225603310,-23415860512,-200117753530,-863731324836,-2486101104594,-3511206832184,11171231626806,110034261679044,500062779185198

%N 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)=0, k=-2 and l=0.

%H Robert Israel, <a href="/A177110/b177110.txt">Table of n, a(n) for n = 0..1739</a>

%F G.f: (1-z + sqrt(1-6*z+13*z^2+4*z^3-4*z^4))/(2*(z-z^2)).

%F D-finite with recurrence: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +3*(-3*n+4)*a(n-3) +2*(-4*n+17)*a(n-4) +4*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016

%F Recurrence follows from the differential equation -1+5*z+3*z^2-5*z^3+2*z^4 + (1-5*z+9*z^2-15*z^3+2*z^4)*g(z) + (z-7*z^2+19*z^3-9*z^4-8*z^5+4*z^6)*g'(z) satisfied by the g.f. - _Robert Israel_, Jul 14 2017

%e a(2)=2*1*0-4=-4. a(3)=2*1*(-4)-4+0^2-2=-14. a(4)=2*1*(-14)-4+2*0*(-4)-4=-36.

%p l:=0: : k := -2 : m:=0: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 :

%p 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);

%K easy,sign

%O 0,3

%A _Richard Choulet_, May 03 2010

%E G.f. edited, and more terms, from _Robert Israel_, Jul 14 2017