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%I #5 Jan 20 2014 22:19:36
%S 1,6,13,64,287,1515,8143,46030,265909,1572193,9443997,57529101,
%T 354394057,2204333079,13823770729,87311462772,554904606279,
%U 3546103422655,22772157825695,146876986425311,951065019090195
%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)=6, 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) +(2-7*n)*a(n-1) +(19-5*n)*a(n-2) +(43*n-134)*a(n-3) +4*(53-13*n)*a(n-4) +20*(n-5)*a(n-5)=0. - _R. J. Mathar_, Jul 24 2012
%e a(2)=2*1*6+2-1=13. a(3)=2*1*13+36+2+1-1=64.
%p l:=-1: : k := 1 : m:=6: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. A176832.
%K easy,nonn
%O 0,2
%A _Richard Choulet_, May 04 2010