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A177169 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.

%I A177169 #5 Jun 14 2016 12:49:58
%S A177169 1,7,12,71,308,1752,9518,55995,331024,2018056,12445114,77971468,
%T A177169 493457274,3154471374,20324817414,131901428431,861253742060,
%U A177169 5654523909972,37304630338790,247183333507140,1644269062695294
%N A177169 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 A177169 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 A177169 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 A177169 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 A177169 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 A177169 Cf. A177168.
%K A177169 easy,nonn
%O A177169 0,2
%A A177169 _Richard Choulet_, May 04 2010