A177169 - OEIS

%I #5 Jun 14 2016 12:49:58

%S 1,7,12,71,308,1752,9518,55995,331024,2018056,12445114,77971468,

%T 493457274,3154471374,20324817414,131901428431,861253742060,

%U 5654523909972,37304630338790,247183333507140,1644269062695294

%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)=7, k=0 and l=-2.

%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=0, l=-2).

%F Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +5*(-3*n+7)*a(n-2) +2*(26*n-81)*a(n-3) +32*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Jun 14 2016

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

%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. A177168.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 04 2010