A176964 - OEIS

%I #5 Mar 02 2016 15:18:44

%S 1,3,5,17,61,245,1021,4405,19453,87589,400541,1855493,8689213,

%T 41068965,195659357,938623045,4530198013,21982331237,107178047773,

%U 524805028357,2579684059581,12724878633765,62968424313821,312503657989317

%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)=3, k=-1 and l=1.

%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=-1, l=1).

%F Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(7*n-5)*a(n-2) +3*(5*n-18)*a(n-3) +24*(-n+4)*a(n-4) +8*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016

%e a(2)=2*1*3-2+1=5. a(3)=2*1*5-2+3^2-1+1=17. a(4)=2*1*17-2+2*3*5-2+1=61.

%p l:=1: : k := -1 : m:=3: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. A176962.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, Apr 29 2010