A177124 - OEIS

%I #5 Mar 02 2016 15:28:13

%S 1,8,19,106,521,3105,18581,117884,761515,5044963,33928351,231507527,

%T 1597241595,11128224961,78169076699,553043148982,3937226978193,

%U 28184931742741,202753591947237,1464948626336061,10626428189078521

%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)=8, 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) +(-13*n+35)*a(n-2) +(59*n-178)*a(n-3) +60*(-n+4)*a(n-4) +20*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016

%e a(2)=2*1*8+2+1=19. a(3)=2*1*19+2+64+1+1=106. a(4)=2*1*106+2+2*8*19+2+1=521.

%p l:=1: : k := 1 : m :=8: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);

%Y Cf. A177123.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 03 2010