A177113 - OEIS

%I #5 Mar 02 2016 15:23:37

%S 1,2,0,-2,-12,-42,-144,-466,-1476,-4522,-13384,-37794,-99964,-237738,

%T -455104,-366706,2555276,20416150,103683976,445363518,1736519252,

%U 6310980502,21595986320,69654711278,210206070236,581729708502

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

%F 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=-2, l=0).

%F Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(11*n-13)*a(n-2) +15*(n-4)*a(n-3) +2*(-16*n+65)*a(n-4) +12*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016

%e a(2)=2*1*2-4=0. a(3)=2*1*0-4+2^2-2=-2. a(4)=2*1*(-2)-4+2*2*0-4=-12.

%p l:=0: : k := -2 : m:=5:d(0):=2: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);

%Y Cf. A177111.

%K easy,sign

%O 0,2

%A _Richard Choulet_, May 03 2010