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A176754 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=0 and l=-2.

%I A176754 #5 Feb 18 2016 14:11:55
%S A176754 1,2,2,6,18,62,218,790,2914,10926,41514,159558,619314,2424414,9561594,
%T A176754 37956726,151548930,608199182,2452070090,9926901670,40338175954,
%U A176754 164471889342,672683135130,2759049956566,11345904429730,46769328002414
%N A176754 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=0 and l=-2.
%F A176754 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 A176754 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +5*(n-1)*a(n-2) +6*(2*n-7)*a(n-3) +12*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Feb 18 2016
%e A176754 a(2)=2*1*2-2=2. a(3)=2*1*2+2^2-2=6. a(4)=2*1*6+2*2*2-2=18.
%p A176754 l:=-2: : k := 0 : m:=2: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 A176754 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 A176754 Cf. A176653.
%K A176754 easy,nonn
%O A176754 0,2
%A A176754 _Richard Choulet_, Apr 25 2010